@@@ ͹ءÃÁ 1*2 + 2*3 + 3*4 + ... + 8*9 = ? @@@
ÍÂÒ¡·ÃÒºÇèÒ Í¹Ø¡ÃÁ 1*2 + 2*3 + 3*4 + ... + 8*9 = ? àËÃͤÃѺ ¾ÍÁÕã¤ÃÃÙéºéÒ§äËÁ ¢Í ÇÔ¸Õ·Ó ´éǹФÃѺ
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áµè¶éÒ¨Ðà¢Õ¹ãËéÁÕËÅÑ¡¡ÒÃ˹èÍ¡ç¤×ÍÁͧÇèÒ $a_n = n(n+1)$ ´Ñ§¹Ñ鹨Ðä´é $a_i = i(i+1)$ áÅéÇ $$S_n = \sum_{i = 1}^{n}i(i+1) = \frac{n(n+1)(n+2)}{3} $$Note. $$\sum_{i = 1}^{n}i = \frac{n(n+1)}{2} $$ $$\sum_{i = 1}^{n}i(i+1) = \frac{n(n+1)(n+2)}{3} $$ $$\sum_{i = 1}^{n}i(i+1)(i+2) = \frac{n(n+1)(n+2)(n+3)}{4} $$ ÊÓËÃѺÇÔ¸Õ¾×é¹°Ò¹¤×Í $$S_n = \sum_{i = 1}^{n}i(i+1) = \sum_{i = 1}^{n}i^2 + \sum_{i = 1}^{n}i = \frac{n(n+1)(2n+1)}{6} + \frac{n(n+1)}{2} = \frac{n(n+1)(n+2)}{3}$$ ã¹·Õè¹Õéµéͧ¡ÒÃËÒ $S_8$ ¡çá·¹ n = 8 ŧã¹Êٵà |
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Attachment 3162 Attachment 3163 |
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