Summation
回答 (3)
2013-06-20 11:51 pm
✔ 最佳答案
有乜野唔明或者有野想問，可以補充問題。希望我嘅答案可以幫到你^ ^圖片參考：http://i.imgur.com/lQhhBYz.png
2013-06-20 15:52:36 補充：
#002：
題目是要你推算一個公式出來，不是要你證明那條公式，請從零開始找起。
2013-06-20 9:02 am
1³+2³+3³+...+n³ = (1+2+3+...+n)²
this can be proven by Mathematical Induction (M.I.)
1+2+3+,,,+n = n(n+1)/2 (this can also be proven by M.I.)
therefore,
1³+2³+3³+...+n³ = [n(n+1)/2]² = n²(n+1)²/4
this can be proven by Mathematical Induction (M.I.)
1+2+3+,,,+n = n(n+1)/2 (this can also be proven by M.I.)
therefore,
1³+2³+3³+...+n³ = [n(n+1)/2]² = n²(n+1)²/4
參考: myself
2013-06-20 3:29 am
(n^2)[(1+n)^2]/4
收錄日期: 2021-04-23 22:04:16
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20130619000051KK00295