{"id":300343,"date":"2023-12-28T21:18:11","date_gmt":"2023-12-28T14:18:11","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=300343"},"modified":"2023-12-28T21:18:11","modified_gmt":"2023-12-28T14:18:11","slug":"cong-thuc-tinh-tong-day-so-cach-deu","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-tinh-tong-day-so-cach-deu\/","title":{"rendered":"C\u00f4ng th\u1ee9c t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u v\u00e0 d\u00e3y s\u1ed1 kh\u00f4ng c\u00e1ch \u0111\u1ec1u ch\u00ednh x\u00e1c nh\u1ea5t"},"content":{"rendered":"<p><strong>C\u00f4ng th\u1ee9c t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u<\/strong> v\u00e0 kh\u00f4ng c\u00e1ch \u0111\u1ec1u \u0111\u01b0\u1ee3c r\u1ea5t nhi\u1ec1u \u0111\u1ed9c gi\u1ea3 t\u00ecm ki\u1ebfm trong th\u1eddi \u0111i\u1ec3m hi\u1ec7n t\u1ea1i. C\u1ea3 hai \u0111\u1ec1u l\u00e0 c\u00f4ng th\u1ee9c quan tr\u1ecdng, y\u00eau c\u1ea7u h\u1ecdc sinh hi\u1ec3u r\u00f5 quy lu\u1eadt h\u00ecnh th\u00e0nh c\u1ee7a d\u00e3y s\u1ed1 \u0111\u1ec3 c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng hi\u1ec7u qu\u1ea3. Trong b\u00e0i vi\u1ebft n\u00e0y, Ho\u00e0ng H\u00e0 Mobile s\u1ebd gi\u00fap b\u1ea1n hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 c\u1ea3 hai c\u00f4ng th\u1ee9c n\u00e0y k\u00e8m v\u00ed d\u1ee5 minh h\u1ecda d\u1ec5 hi\u1ec3u nh\u1ea5t.<\/p>\n<h2>B\u00e0i to\u00e1n t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 l\u00e0 g\u00ec?<\/h2>\n<p>Tr\u01b0\u1edbc khi t\u00ecm hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 c\u00e1c <strong>c\u00f4ng th\u1ee9c t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u<\/strong> v\u00e0 kh\u00f4ng c\u00e1ch \u0111\u1ec1u, ch\u00fang ta n\u00ean hi\u1ec3u r\u00f5 b\u00e0i to\u00e1n t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 l\u00e0 g\u00ec. V\u1ec1 c\u01a1 b\u1ea3n, b\u00e0i to\u00e1n t\u00ednh t\u1ed5ng m\u1ed9t d\u00e3y s\u1ed1 l\u00e0 vi\u1ec7c t\u00ednh t\u1ed5ng c\u00e1c gi\u00e1 tr\u1ecb s\u1ed1 h\u1ecdc trong m\u1ed9t chu\u1ed7i ho\u1eb7c d\u00e3y s\u1ed1 c\u1ee5 th\u1ec3. D\u00e3y s\u1ed1 c\u00f3 th\u1ec3 bao g\u1ed3m c\u00e1c s\u1ed1 nguy\u00ean, s\u1ed1 th\u1ef1c, ho\u1eb7c c\u00e1c lo\u1ea1i s\u1ed1 kh\u00e1c, v\u00e0 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh theo m\u1ed9t quy t\u1eafc nh\u1ea5t \u0111\u1ecbnh ho\u1eb7c \u0111\u01a1n gi\u1ea3n l\u00e0 m\u1ed9t danh s\u00e1ch s\u1ed1 cho tr\u01b0\u1edbc.<\/p>\n<figure id=\"attachment_300350\" aria-describedby=\"caption-attachment-300350\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img fetchpriority=\"high\" decoding=\"async\" class=\"wp-image-300350 size-full webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu.jpg\" alt=\"cong-thuc-tinh-tong-day-so-cach-deu\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><figcaption id=\"caption-attachment-300350\" class=\"wp-caption-text\"><em>H\u00ecnh \u1ea3nh minh h\u1ecda b\u00e0i to\u00e1n t\u00ednh t\u1ed5ng c\u1ee7a d\u00e3y s\u1ed1 b\u1ea5t k\u00ec<\/em><\/figcaption><\/figure>\n<p>C\u00f3 nhi\u1ec1u c\u00e1ch \u0111\u1ec3 t\u00ednh t\u1ed5ng n\u00e0y, t\u00f9y thu\u1ed9c v\u00e0o lo\u1ea1i d\u00e3y s\u1ed1 v\u00e0 m\u1ee5c \u0111\u00edch s\u1eed d\u1ee5ng:<\/p>\n<p><strong>T\u1ed5ng tr\u1ef1c ti\u1ebfp<\/strong>: \u0110\u00e2y l\u00e0 c\u00e1ch \u0111\u01a1n gi\u1ea3n nh\u1ea5t, \u0111\u00f3 l\u00e0 b\u1ea1n c\u1ed9ng t\u1eebng s\u1ed1 trong d\u00e3y l\u1ea1i v\u1edbi nhau. V\u00ed d\u1ee5, t\u1ed5ng c\u1ee7a d\u00e3y s\u1ed1 1, 2, 3, 4 l\u00e0 1 + 2 + 3 + 4 = 10.<\/p>\n<p><strong>C\u00f4ng th\u1ee9c t\u1ed5ng qu\u00e1t<\/strong>: \u0110\u1ed1i v\u1edbi m\u1ed9t s\u1ed1 d\u00e3y s\u1ed1 \u0111\u1eb7c bi\u1ec7t (nh\u01b0 d\u00e3y s\u1ed1 c\u1ea5p s\u1ed1 c\u1ed9ng ho\u1eb7c c\u1ea5p s\u1ed1 nh\u00e2n), c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc \u0111\u1ec3 t\u00ednh t\u1ed5ng m\u00e0 kh\u00f4ng c\u1ea7n ph\u1ea3i c\u1ed9ng t\u1eebng s\u1ed1. V\u00ed d\u1ee5, t\u1ed5ng c\u1ee7a d\u00e3y s\u1ed1 c\u1ea5p s\u1ed1 c\u1ed9ng t\u1eeb 1 \u0111\u1ebfn n l\u00e0 (n * (n + 1)) \/ 2.<\/p>\n<p><strong>S\u1eed d\u1ee5ng l\u1eadp tr\u00ecnh<\/strong>: Trong l\u1eadp tr\u00ecnh m\u00e1y t\u00ednh, c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng v\u00f2ng l\u1eb7p \u0111\u1ec3 t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1. \u0110\u00e2y l\u00e0 ph\u01b0\u01a1ng ph\u00e1p ph\u1ed5 bi\u1ebfn khi x\u1eed l\u00fd d\u1eef li\u1ec7u s\u1ed1.<\/p>\n<h2>Ph\u01b0\u01a1ng ph\u00e1p \u00e1p d\u1ee5ng t\u00ednh t\u1ed5ng m\u1ed9t d\u00e3y s\u1ed1 hi\u1ec7u qu\u1ea3<\/h2>\n<p>C\u00e1c ph\u01b0\u01a1ng ph\u00e1p d\u01b0\u1edbi \u0111\u00e2y s\u1ebd gi\u00fap b\u1ea1n d\u1ec5 d\u00e0ng gi\u1ea3i c\u00e1c b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn t\u00ednh t\u1ed5ng m\u1ed9t d\u00e3y s\u1ed1 khi \u00e1p d\u1ee5ng <strong>c\u00f4ng th\u1ee9c t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u<\/strong> ho\u1eb7c kh\u00f4ng c\u00e1ch \u0111\u1ec1u. \u0110\u1ec3 gi\u1ea3i quy\u1ebft b\u00e0i to\u00e1n t\u00ednh t\u1ed5ng m\u1ed9t d\u00e3y s\u1ed1, tr\u01b0\u1edbc h\u1ebft ta c\u1ea7n hi\u1ec3u r\u00f5 quy lu\u1eadt c\u1ee7a d\u00e3y s\u1ed1 \u0111\u00f3. D\u1ef1a v\u00e0o quy lu\u1eadt, ta c\u00f3 th\u1ec3 x\u00e1c \u0111\u1ecbnh c\u00e1ch t\u00ednh t\u1ed5ng m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c v\u00e0 hi\u1ec7u qu\u1ea3.<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-1.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-1-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-1-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"size-full wp-image-300351 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-1.jpg\" alt=\"cong-thuc-tinh-tong-day-so-cach-deu-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 quy lu\u1eadt ph\u1ed5 bi\u1ebfn c\u00f9ng v\u1edbi c\u00e1ch ti\u1ebfp c\u1eadn \u0111\u1ec3 t\u00ednh t\u1ed5ng:<\/p>\n<p><strong>C\u1ea5p s\u1ed1 c\u1ed9ng<\/strong>: M\u1ed7i s\u1ed1 h\u1ea1ng sau b\u1eb1ng s\u1ed1 h\u1ea1ng tr\u01b0\u1edbc c\u1ed9ng th\u00eam m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean a. V\u00ed d\u1ee5: 2, 4, 6, 8,&#8230; \u1edf \u0111\u00e2y a = 2. T\u1ed5ng c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00ednh nhanh b\u1eb1ng c\u00f4ng th\u1ee9c \u0111\u1eb7c bi\u1ec7t c\u1ee7a c\u1ea5p s\u1ed1 c\u1ed9ng.<\/p>\n<p><strong>C\u1ea5p s\u1ed1 nh\u00e2n<\/strong>: M\u1ed7i s\u1ed1 h\u1ea1ng sau b\u1eb1ng s\u1ed1 h\u1ea1ng tr\u01b0\u1edbc nh\u00e2n v\u1edbi m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean q kh\u00e1c 0. V\u00ed d\u1ee5: 3, 9, 27, 81,&#8230; \u1edf \u0111\u00e2y q = 3. T\u1ed5ng c\u0169ng c\u00f3 c\u00f4ng th\u1ee9c ri\u00eang d\u00e0nh cho c\u1ea5p s\u1ed1 nh\u00e2n.<\/p>\n<p><strong>D\u00e3y s\u1ed1 Fibonacci<\/strong>: M\u1ed7i s\u1ed1 h\u1ea1ng t\u1eeb th\u1ee9 3 tr\u1edf \u0111i b\u1eb1ng t\u1ed5ng hai s\u1ed1 h\u1ea1ng li\u1ec1n tr\u01b0\u1edbc. V\u00ed d\u1ee5: 1, 1, 2, 3, 5, 8,&#8230; T\u1ed5ng \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng c\u00e1ch c\u1ed9ng t\u1eebng s\u1ed1 h\u1ea1ng.<\/p>\n<p><strong>Quy lu\u1eadt t\u1ed5ng h\u1ee3p<\/strong>: C\u00f3 nh\u1eefng quy lu\u1eadt ph\u1ee9c t\u1ea1p h\u01a1n, nh\u01b0 m\u1ed7i s\u1ed1 h\u1ea1ng b\u1eb1ng t\u1ed5ng c\u1ee7a s\u1ed1 h\u1ea1ng tr\u01b0\u1edbc c\u1ed9ng v\u1edbi m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean d v\u00e0 s\u1ed1 th\u1ee9 t\u1ef1 c\u1ee7a n\u00f3. V\u00ed d\u1ee5: 2, 5, 9, 14,&#8230; \u1edf \u0111\u00e2y d = 2.<\/p>\n<p><strong>Nh\u00e2n v\u1edbi s\u1ed1 th\u1ee9 t\u1ef1<\/strong>: M\u1ed7i s\u1ed1 h\u1ea1ng sau b\u1eb1ng s\u1ed1 h\u1ea1ng tr\u01b0\u1edbc nh\u00e2n v\u1edbi s\u1ed1 th\u1ee9 t\u1ef1 c\u1ee7a n\u00f3. V\u00ed d\u1ee5: 2, 4, 12, 48,&#8230; \u1edf \u0111\u00e2y s\u1ed1 h\u1ea1ng \u0111\u1ea7u ti\u00ean l\u00e0 2.<\/p>\n<h2>C\u00f4ng th\u1ee9c t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u chi ti\u1ebft, hi\u1ec7u qu\u1ea3 nh\u1ea5t<\/h2>\n<p>Khi b\u1ea1n mu\u1ed1n t\u00ednh t\u1ed5ng m\u1ed9t d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u, \u0111\u00e2y l\u00e0 c\u00e1ch l\u00e0m \u0111\u01a1n gi\u1ea3n v\u00e0 th\u00fa v\u1ecb m\u00e0 b\u1ea1n c\u00f3 th\u1ec3 th\u1eed:<\/p>\n<h3>T\u00ednh s\u1ed1 s\u1ed1 h\u1ea1ng xu\u1ea5t hi\u1ec7n trong d\u00e3y<\/h3>\n<p>Ch\u00fang ta b\u1eaft \u0111\u1ea7u b\u1eb1ng vi\u1ec7c t\u00ecm ra c\u00f3 bao nhi\u00eau s\u1ed1 trong d\u00e3y. C\u00f4ng th\u1ee9c nh\u01b0 sau:<\/p>\n<p><strong>S\u1ed1 S\u1ed1 H\u1ea1ng = (S\u1ed1 H\u1ea1ng Cu\u1ed1i &#8211; S\u1ed1 H\u1ea1ng \u0110\u1ea7u) \/ \u0110\u01a1n V\u1ecb Kho\u1ea3ng C\u00e1ch + 1<\/strong><\/p>\n<p>V\u00ed d\u1ee5: X\u00e9t d\u00e3y s\u1ed1 t\u1eeb 1 \u0111\u1ebfn 100. S\u1ed1 s\u1ed1 h\u1ea1ng l\u00e0 (100 &#8211; 1) \/ 1 + 1 = 100.<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-2.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-2-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-2-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"size-full wp-image-300348 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-2.jpg\" alt=\"cong-thuc-tinh-tong-day-so-cach-deu-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<h3>T\u00ednh t\u1ed5ng cho d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u nhau<\/h3>\n<p>B\u00e2y gi\u1edd, \u0111\u1ec3 t\u00ednh t\u1ed5ng, ta s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c:<\/p>\n<p><strong>T\u1ed5ng D\u00e3y S\u1ed1 = (S\u1ed1 H\u1ea1ng \u0110\u1ea7u + S\u1ed1 H\u1ea1ng Cu\u1ed1i) x S\u1ed1 S\u1ed1 H\u1ea1ng \/ 2<\/strong><\/p>\n<p>V\u00ed d\u1ee5: V\u1edbi d\u00e3y s\u1ed1 t\u1eeb 2 \u0111\u1ebfn 50 c\u00e1ch \u0111\u1ec1u 2 \u0111\u01a1n v\u1ecb, t\u1ed5ng l\u00e0 (2 + 50) x 25 \/ 2 = 650.<\/p>\n<h3>T\u00ecm s\u1ed1 h\u1ea1ng cu\u1ed1i<\/h3>\n<p>N\u1ebfu b\u1ea1n bi\u1ebft s\u1ed1 h\u1ea1ng \u0111\u1ea7u v\u00e0 s\u1ed1 l\u01b0\u1ee3ng s\u1ed1 h\u1ea1ng, b\u1ea1n c\u00f3 th\u1ec3 t\u00ecm s\u1ed1 h\u1ea1ng cu\u1ed1i:<\/p>\n<p><strong>S\u1ed1 H\u1ea1ng Cu\u1ed1i = S\u1ed1 H\u1ea1ng \u0110\u1ea7u + (S\u1ed1 S\u1ed1 H\u1ea1ng &#8211; 1) x \u0110\u01a1n V\u1ecb Kho\u1ea3ng C\u00e1ch<\/strong><\/p>\n<p>V\u00ed d\u1ee5: Trong d\u00e3y s\u1ed1 1, 3, 5,&#8230; c\u00f3 25 s\u1ed1 h\u1ea1ng, s\u1ed1 cu\u1ed1i l\u00e0 1 + (25 &#8211; 1) x 2 = 49.<\/p>\n<h3>T\u00ecm s\u1ed1 h\u1ea1ng \u0111\u1ea7u khi \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u<\/h3>\n<p>Ng\u01b0\u1ee3c l\u1ea1i, n\u1ebfu bi\u1ebft s\u1ed1 h\u1ea1ng cu\u1ed1i v\u00e0 s\u1ed1 l\u01b0\u1ee3ng s\u1ed1 h\u1ea1ng, b\u1ea1n c\u00f3 th\u1ec3 t\u00ecm s\u1ed1 h\u1ea1ng \u0111\u1ea7u:<\/p>\n<p><strong>S\u1ed1 H\u1ea1ng \u0110\u1ea7u = S\u1ed1 H\u1ea1ng Cu\u1ed1i &#8211; (S\u1ed1 S\u1ed1 H\u1ea1ng &#8211; 1) x \u0110\u01a1n V\u1ecb Kho\u1ea3ng C\u00e1ch<\/strong><\/p>\n<p>V\u00ed d\u1ee5: N\u1ebfu d\u00e3y s\u1ed1 c\u00f3 50 s\u1ed1 h\u1ea1ng, s\u1ed1 cu\u1ed1i l\u00e0 100 v\u00e0 kho\u1ea3ng c\u00e1ch l\u00e0 2, s\u1ed1 \u0111\u1ea7u l\u00e0 100 &#8211; (50 &#8211; 1) x 2 = 2.<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-3.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-3-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-3-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-300347 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-3.jpg\" alt=\"cong-thuc-tinh-tong-day-so-cach-deu-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<h3>T\u00ednh trung b\u00ecnh c\u1ed9ng<\/h3>\n<p>\u0110\u00f4i khi b\u1ea1n mu\u1ed1n bi\u1ebft trung b\u00ecnh c\u1ee7a d\u00e3y s\u1ed1 th\u00ec \u0111\u00e2y l\u00e0 c\u00e1ch m\u00e0 b\u1ea1n c\u00f3 th\u1ec3 th\u1ef1c hi\u1ec7n:<\/p>\n<p><strong>Trung B\u00ecnh C\u1ed9ng = T\u1ed5ng D\u00e3y S\u1ed1 \/ S\u1ed1 S\u1ed1 H\u1ea1ng<\/strong><\/p>\n<p>V\u00ed d\u1ee5: Trung b\u00ecnh c\u1ed9ng c\u1ee7a d\u00e3y s\u1ed1 t\u1eeb 1 \u0111\u1ebfn 100 l\u00e0 5050 \/ 100 = 50.5.<\/p>\n<h3>L\u01b0u \u00fd khi \u00e1p d\u1ee5ng<\/h3>\n<p>C\u00e1c <strong>c\u00f4ng th\u1ee9c t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u<\/strong> tr\u00ean gi\u00fap b\u1ea1n nhanh ch\u00f3ng t\u00ecm ra \u0111\u00e1p s\u1ed1 m\u00e0 kh\u00f4ng c\u1ea7n ph\u1ea3i c\u1ed9ng t\u1eebng s\u1ed1 m\u1ed9t, ti\u1ebft ki\u1ec7m th\u1eddi gian v\u00e0 c\u00f4ng s\u1ee9c, \u0111\u1eb7c bi\u1ec7t h\u1eefu \u00edch khi l\u00e0m vi\u1ec7c v\u1edbi d\u00e3y s\u1ed1 d\u00e0i. Tuy nhi\u00ean c\u0169ng c\u00f3 m\u1ed9t s\u1ed1 l\u01b0u \u00fd m\u00e0 b\u1ea1n c\u1ea7n n\u1eafm r\u00f5 nh\u01b0:<\/p>\n<ul>\n<li>\u0110\u1ea7u ti\u00ean, h\u00e3y nh\u1edb r\u1eb1ng b\u1ea1n c\u1ea7n x\u00e1c \u0111\u1ecbnh ba y\u1ebfu t\u1ed1 ch\u00ednh: s\u1ed1 h\u1ea1ng \u0111\u1ea7u, s\u1ed1 h\u1ea1ng cu\u1ed1i, v\u00e0 t\u1ed5ng s\u1ed1 s\u1ed1 h\u1ea1ng trong d\u00e3y. \u0110\u1eebng qu\u00ean c\u1ea3 kho\u1ea3ng c\u00e1ch gi\u1eefa hai s\u1ed1 li\u00ean ti\u1ebfp.<\/li>\n<li>N\u1ebfu d\u00e3y s\u1ed1 c\u1ee7a b\u1ea1n c\u00f3 s\u1ed1 l\u01b0\u1ee3ng s\u1ed1 h\u1ea1ng l\u00e0 s\u1ed1 l\u1ebb, b\u1ea1n s\u1ebd th\u1ea5y r\u1eb1ng s\u1ed1 h\u1ea1ng \u1edf gi\u1eefa c\u00f3 th\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c d\u1ec5 d\u00e0ng. C\u00f4ng th\u1ee9c l\u00e0 (s\u1ed1 cu\u1ed1i + s\u1ed1 \u0111\u1ea7u) \/ 2. \u0110i\u1ec1u n\u00e0y gi\u00fap b\u1ea1n nhanh ch\u00f3ng t\u00ecm ra gi\u00e1 tr\u1ecb trung t\u00e2m c\u1ee7a d\u00e3y s\u1ed1.<\/li>\n<li>Ch\u00fa \u00fd r\u1eb1ng, t\u00f9y thu\u1ed9c v\u00e0o d\u00e3y s\u1ed1 c\u1ee7a b\u1ea1n c\u00f3 t\u0103ng d\u1ea7n hay gi\u1ea3m d\u1ea7n, c\u00e1ch \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c c\u00f3 th\u1ec3 thay \u0111\u1ed5i. \u0110\u1ed1i v\u1edbi d\u00e3y s\u1ed1 gi\u1ea3m d\u1ea7n, b\u1ea1n c\u00f3 th\u1ec3 c\u1ea7n \u0111\u1ea3o ng\u01b0\u1ee3c c\u00e1ch t\u00ednh s\u1ed1 h\u1ea1ng \u0111\u1ea7u v\u00e0 cu\u1ed1i khi s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c.<\/li>\n<\/ul>\n<p>V\u1edbi nh\u1eefng l\u01b0u \u00fd n\u00e0y, b\u1ea1n s\u1ebd t\u1ef1 tin h\u01a1n trong vi\u1ec7c gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 v\u00e0 \u00e1p d\u1ee5ng c\u00e1c c\u00f4ng th\u1ee9c m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c. Ch\u00fac b\u1ea1n th\u00e0nh c\u00f4ng!<\/p>\n<h2>C\u00f4ng th\u1ee9c t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 kh\u00f4ng c\u00e1ch \u0111\u1ec1u<\/h2>\n<p>Khi b\u1ea1n \u0111\u1ed1i m\u1eb7t v\u1edbi d\u00e3y s\u1ed1 kh\u00f4ng c\u00e1ch \u0111\u1ec1u, nh\u01b0 d\u00e3y s\u1ed1 Fibonacci ho\u1eb7c c\u00e1c d\u00e3y s\u1ed1 c\u00f3 quy t\u1eafc ri\u00eang, vi\u1ec7c t\u00ecm c\u00f4ng th\u1ee9c t\u1ed5ng c\u00f3 th\u1ec3 tr\u1edf n\u00ean th\u00fa v\u1ecb v\u00e0 \u0111\u00f4i khi ph\u1ee9c t\u1ea1p.<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-4.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-4-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-4-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-300346 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-4.jpg\" alt=\"cong-thuc-tinh-tong-day-so-cach-deu-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><strong>V\u00ed d\u1ee5: T\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 kh\u00f4ng c\u00e1ch \u0111\u1ec1u<\/strong><\/p>\n<p>X\u00e9t b\u00e0i to\u00e1n: T\u00ednh A = 1 x 2 + 2 x 3 + 3 x 4 +\u2026+ n x (n + 1).<\/p>\n<p>L\u1eddi Gi\u1ea3i:<\/p>\n<p>Ch\u00fang ta s\u1ebd d\u00f9ng m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p \u0111\u1eb7c bi\u1ec7t \u0111\u1ec3 gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 n\u00e0y. \u0110\u1ea7u ti\u00ean, ta nh\u00e2n c\u1ea3 d\u00e3y s\u1ed1 v\u1edbi 3:<\/p>\n<p><strong>3 x A<\/strong> = 1 x 2 x 3 + 2 x 3 x 3 + 3 x 4 x 3 +\u2026+ n x (n + 1) x 3<\/p>\n<p>Khi m\u1edf r\u1ed9ng v\u00e0 s\u1eafp x\u1ebfp l\u1ea1i c\u00e1c s\u1ed1 h\u1ea1ng, ta c\u00f3:<\/p>\n<p>3 x A = 1 x 2 x (3 \u2013 0) + 2 x 3 x (4 \u2013 1) + 3 x 4 x (5 \u2013 2) +\u2026+ n x (n + 1) x [(n + 2) \u2013 (n \u2013 1)]<\/p>\n<p>D\u00e3y s\u1ed1 n\u00e0y \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp l\u1ea1i th\u00e0nh:<\/p>\n<p>3 x A = 1 x 2 x 3 + 2 x 3 x 4 \u2013 1 x 2 x 3 + 3 x 4 x 5 \u2013 2 x 3 x 4 +\u2026+ n x (n + 1) x (n + 2) \u2013 (n \u2013 1) x n x (n + 1)<\/p>\n<p>Khi b\u1ea1n xem x\u00e9t k\u1ef9 c\u00e0ng, b\u1ea1n s\u1ebd th\u1ea5y r\u1eb1ng m\u1ed9t s\u1ed1 s\u1ed1 h\u1ea1ng s\u1ebd b\u1ecb h\u1ee7y b\u1ecf l\u1eabn nhau. K\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng s\u1ebd ch\u1ec9 c\u00f2n l\u1ea1i:<\/p>\n<p><strong>3 x A<\/strong> = n x (n + 1) x (n + 2)<\/p>\n<p>V\u00e0 cu\u1ed1i c\u00f9ng, chia c\u1ea3 hai b\u00ean cho 3 \u0111\u1ec3 t\u00ecm A:<\/p>\n<p><strong>A<\/strong> = n x (n + 1) x (n + 2) \/ 3<\/p>\n<h2>M\u1ed9t s\u1ed1 b\u00e0i to\u00e1n t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 kh\u00f4ng c\u00e1ch \u0111\u1ec1u v\u00e0 c\u00e1ch \u0111\u1ec1u<\/h2>\n<p>Sau khi t\u00ecm hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 <strong>c\u00f4ng th\u1ee9c t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u<\/strong> v\u00e0 kh\u00f4ng c\u00e1ch \u0111\u1ec1u, b\u1ea1n n\u00ean tham kh\u1ea3o c\u00e1c b\u00e0i t\u1eadp b\u00ean d\u01b0\u1edbi \u0111\u1ec3 \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c hi\u1ec7u qu\u1ea3 h\u01a1n:<\/p>\n<h3>B\u00e0i t\u1eadp t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u<\/h3>\n<p>Khi b\u1ea1n l\u00e0m b\u00e0i t\u1eadp t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u, m\u1ed9t s\u1ed1 v\u00ed d\u1ee5 c\u1ee5 th\u1ec3 sau \u0111\u00e2y s\u1ebd gi\u00fap b\u1ea1n hi\u1ec3u r\u00f5 h\u01a1n c\u00e1ch ti\u1ebfp c\u1eadn v\u00e0 gi\u1ea3i quy\u1ebft:<\/p>\n<p><strong>B\u00e0i t\u1eadp 1: T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a T v\u1edbi T = 2 + 3 + 4 + 5 +\u2026+ 2015<\/strong><\/p>\n<p><u>L\u1eddi gi\u1ea3i:<\/u><\/p>\n<p>T\u00ednh s\u1ed1 s\u1ed1 h\u1ea1ng: S\u1ed1 s\u1ed1 h\u1ea1ng trong d\u00e3y l\u00e0 (2015 \u2013 2) \/ 1 + 1 = 2014.<\/p>\n<p>T\u00ednh t\u1ed5ng: T = (2015 + 2) x 2014 \/ 2 = 2,030,042.<\/p>\n<p>\u0110\u00e1p s\u1ed1: 2,030,042<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-5.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-5-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-5-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-300345 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-5.jpg\" alt=\"cong-thuc-tinh-tong-day-so-cach-deu-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><strong>B\u00e0i t\u1eadp 2: T\u00ednh t\u1ed5ng 40 s\u1ed1 l\u1ebb li\u00ean ti\u1ebfp, bi\u1ebft s\u1ed1 l\u1ebb l\u1edbn nh\u1ea5t l\u00e0 2011.<\/strong><\/p>\n<p><u>L\u1eddi gi\u1ea3i:<\/u><\/p>\n<p>T\u00ecm s\u1ed1 l\u1ebb nh\u1ecf nh\u1ea5t: S\u1ed1 l\u1ebb nh\u1ecf nh\u1ea5t l\u00e0 2011 \u2013 (40 \u2013 1) x 2 = 1933.<\/p>\n<p>T\u00ednh t\u1ed5ng: T\u1ed5ng c\u1ee7a 40 s\u1ed1 l\u1ebb = (2011 + 1933) x 40 \/ 2 = 78,880.<\/p>\n<p>\u0110\u00e1p s\u1ed1: 78,880<\/p>\n<p><strong>B\u00e0i t\u1eadp 3: M\u1ed9t khu ph\u1ed1 c\u00f3 25 nh\u00e0 v\u1edbi s\u1ed1 nh\u00e0 l\u00e0 c\u00e1c s\u1ed1 l\u1ebb li\u00ean ti\u1ebfp, t\u1ed5ng s\u1ed1 nh\u00e0 l\u00e0 1145. H\u1ecfi s\u1ed1 nh\u00e0 \u0111\u1ea7u ti\u00ean l\u00e0 bao nhi\u00eau?<\/strong><\/p>\n<p><u>L\u1eddi gi\u1ea3i:<\/u><\/p>\n<p>T\u00ednh trung b\u00ecnh c\u1ed9ng: Trung b\u00ecnh c\u1ed9ng c\u1ee7a d\u00e3y s\u1ed1 l\u00e0 1145 \/ 25 = 45,8.<\/p>\n<p>T\u00ecm s\u1ed1 nh\u00e0 \u0111\u1ea7u ti\u00ean: S\u1ed1 nh\u00e0 \u0111\u1ea7u ti\u00ean = 45,8 \u2013 (25 \u2013 1) x 2 \/ 2 = 9.<\/p>\n<p>\u0110\u00e1p s\u1ed1: 9<\/p>\n<p><strong>L\u01b0u \u00fd:<\/strong><\/p>\n<ul>\n<li>S\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u: T = (S\u1ed1 H\u1ea1ng \u0110\u1ea7u + S\u1ed1 H\u1ea1ng Cu\u1ed1i) x S\u1ed1 S\u1ed1 H\u1ea1ng \/ 2.<\/li>\n<li>Lu\u00f4n ki\u1ec3m tra k\u1ef9 s\u1ed1 h\u1ea1ng \u0111\u1ea7u v\u00e0 cu\u1ed1i c\u0169ng nh\u01b0 s\u1ed1 l\u01b0\u1ee3ng s\u1ed1 h\u1ea1ng trong d\u00e3y.<\/li>\n<li>H\u00e3y th\u1eed l\u00e0m th\u00eam nhi\u1ec1u b\u00e0i t\u1eadp kh\u00e1c nhau \u0111\u1ec3 n\u1eafm v\u1eefng c\u00e1ch s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c.<\/li>\n<\/ul>\n<h3>B\u00e0i t\u1eadp t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 kh\u00f4ng c\u00e1ch \u0111\u1ec1u<\/h3>\n<p>B\u00ean c\u1ea1nh c\u00e1c b\u00e0i t\u1eadp li\u00ean quan \u0111\u1ebfn <strong>c\u00f4ng th\u1ee9c t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u<\/strong>, d\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp \u0111\u1ec3 luy\u1ec7n c\u00f4ng th\u1ee9c t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 kh\u00f4ng c\u00e1ch \u0111\u1ec1u m\u00e0 b\u1ea1n c\u00f3 th\u1ec3 tham kh\u1ea3o:<\/p>\n<p><strong>B\u00e0i T\u1eadp 1: T\u00ednh M = 1 x 2 x 3 + 2 x 3 x 4 +\u2026+ (n \u2013 1) x n x (n + 1).<\/strong><\/p>\n<p><u>L\u1eddi gi\u1ea3i:<\/u><\/p>\n<p>Nh\u00e2n M v\u1edbi 4 v\u00e0 s\u1eafp x\u1ebfp l\u1ea1i:<\/p>\n<p>4 x M = 1 x 2 x 3 x 4 + 2 x 3 x 4 x 5 +\u2026+ (n \u2013 1) x n x (n + 1) x (n + 2) \u2013 (n \u2013 2) x (n \u2013 1) x n x (n + 1).<\/p>\n<p>K\u1ebft qu\u1ea3:<\/p>\n<p>M = [(n \u2013 1) x n x (n + 1) x (n + 2)] \/ 4.<\/p>\n<p>\u0110\u00e1p s\u1ed1: M = (n \u2013 1) x n x (n + 1) x (n + 2) \/ 4<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-6.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-6-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-6-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-300344 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-6.jpg\" alt=\"cong-thuc-tinh-tong-day-so-cach-deu-6\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-6-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-tinh-tong-day-so-cach-deu-6-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><strong>B\u00e0i T\u1eadp 2: T\u00ednh N = 1 x 4 + 2 x 5 + 3 x 6 + 4 x 7 +\u2026+ n x (n + 3).<\/strong><\/p>\n<p><u>L\u1eddi gi\u1ea3i:<\/u><\/p>\n<p>Bi\u1ebfn \u0111\u1ed5i m\u1ed7i s\u1ed1 h\u1ea1ng:<\/p>\n<p>N = 1 x 2 + 2 x 3 + 3 x 4 +\u2026+ n x (n + 1) + (2 + 4 + 6 +\u2026+ 2n).<\/p>\n<p>T\u00ednh t\u1ed5ng d\u00e3y s\u1ed1:<\/p>\n<p>N = n(n + 1)(n + 2)\/3 + (2n + 2)n\/2.<\/p>\n<p>K\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng:<\/p>\n<p>N = n(n + 1)(n + 5)\/3.<\/p>\n<p>\u0110\u00e1p s\u1ed1: N = n(n + 1)(n + 5)\/3<\/p>\n<p><strong>L\u01b0u \u00fd:<\/strong><\/p>\n<ul>\n<li>Vi\u1ec7c bi\u1ebfn \u0111\u1ed5i v\u00e0 s\u1eafp x\u1ebfp l\u1ea1i c\u00e1c s\u1ed1 h\u1ea1ng trong d\u00e3y s\u1ed1 l\u00e0 ch\u00eca kh\u00f3a \u0111\u1ec3 t\u00ecm ra c\u00f4ng th\u1ee9c t\u1ed5ng.<\/li>\n<li>H\u00e3y ch\u1eafc ch\u1eafn r\u1eb1ng m\u1ed7i b\u01b0\u1edbc bi\u1ebfn \u0111\u1ed5i \u0111\u01b0\u1ee3c th\u1ef1c hi\u1ec7n m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c.<\/li>\n<li>C\u00e0ng th\u1ef1c h\u00e0nh nhi\u1ec1u, b\u1ea1n c\u00e0ng d\u1ec5 d\u00e0ng nh\u1eadn ra m\u1eabu s\u1ed1 trong c\u00e1c d\u00e3y s\u1ed1 v\u00e0 \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c m\u1ed9t c\u00e1ch linh ho\u1ea1t.<\/li>\n<\/ul>\n<h2>T\u1ea1m k\u1ebft<\/h2>\n<p>K\u1ebft lu\u1eadn v\u1ec1 b\u00e0i vi\u1ebft <strong>c\u00f4ng th\u1ee9c t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u<\/strong>, ch\u00fang ta c\u00f3 th\u1ec3 th\u1ea5y r\u1eb1ng vi\u1ec7c hi\u1ec3u v\u00e0 \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c n\u00e0y l\u00e0 r\u1ea5t quan tr\u1ecdng trong vi\u1ec7c gi\u1ea3i quy\u1ebft nhi\u1ec1u lo\u1ea1i b\u00e0i to\u00e1n to\u00e1n h\u1ecdc. C\u00f4ng th\u1ee9c n\u00e0y kh\u00f4ng ch\u1ec9 \u0111\u01a1n gi\u1ea3n v\u00e0 d\u1ec5 hi\u1ec3u m\u00e0 c\u00f2n r\u1ea5t h\u1eefu \u00edch trong vi\u1ec7c ti\u1ebft ki\u1ec7m th\u1eddi gian v\u00e0 c\u00f4ng s\u1ee9c khi t\u00ednh t\u1ed5ng m\u1ed9t d\u00e3y s\u1ed1 l\u1edbn. Ngo\u00e0i ra, b\u00e0i vi\u1ebft c\u0169ng cung c\u1ea5p nh\u1eefng v\u00ed d\u1ee5 c\u1ee5 th\u1ec3 v\u00e0 l\u1eddi gi\u1ea3i chi ti\u1ebft, gi\u00fap ng\u01b0\u1eddi b\u1ea1n d\u1ec5 d\u00e0ng hi\u1ec3u v\u00e0 \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c v\u00e0o th\u1ef1c t\u1ebf.<\/p>\n<p>Xem th\u00eam:<\/p>\n<ul>\n<li><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-to-hop-chinh-hop\/\">B\u1ed9 c\u00f4ng th\u1ee9c Ho\u00e1n v\u1ecb \u2013 Ch\u1ec9nh h\u1ee3p \u2013 T\u1ed5 h\u1ee3p \u0111\u1ea7y \u0111\u1ee7 nh\u1ea5t trong To\u00e1n h\u1ecdc<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/the-tich-khoi-cau\/\">C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh c\u1ea7u v\u00e0 di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u<\/a><\/strong><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>C\u00f4ng th\u1ee9c t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u v\u00e0 kh\u00f4ng c\u00e1ch \u0111\u1ec1u \u0111\u01b0\u1ee3c r\u1ea5t nhi\u1ec1u \u0111\u1ed9c gi\u1ea3 t\u00ecm ki\u1ebfm trong th\u1eddi \u0111i\u1ec3m hi\u1ec7n t\u1ea1i. C\u1ea3 hai \u0111\u1ec1u l\u00e0 c\u00f4ng th\u1ee9c quan tr\u1ecdng, y\u00eau c\u1ea7u h\u1ecdc sinh hi\u1ec3u r\u00f5 quy lu\u1eadt h\u00ecnh th\u00e0nh c\u1ee7a d\u00e3y s\u1ed1 \u0111\u1ec3 c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng hi\u1ec7u qu\u1ea3. Trong b\u00e0i vi\u1ebft [&hellip;]<\/p>\n","protected":false},"author":83,"featured_media":300349,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3910,30453],"tags":[],"class_list":["post-300343","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-kham-pha","category-kien-thuc"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v24.2 (Yoast SEO v24.2) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>C\u00f4ng th\u1ee9c t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u v\u00e0 d\u00e3y s\u1ed1 kh\u00f4ng c\u00e1ch \u0111\u1ec1u<\/title>\n<meta name=\"description\" content=\"\u0110\u1eebng b\u1ecf qua b\u00e0i vi\u1ebft n\u00e0y n\u1ebfu b\u1ea1n \u0111ang t\u00ecm ki\u1ebfm c\u00f4ng th\u1ee9c t\u00ednh t\u1ed5ng d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u v\u00e0 kh\u00f4ng c\u00e1ch \u0111\u1ec1u hi\u1ec7u qu\u1ea3 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