數學名義變數問題..

2008-09-23 5:40 pm
計算 
n
Σ [k³ - (k - 1)³]
k=1

回答 (1)

2008-09-23 6:11 pm
✔ 最佳答案
Sum of (k -1)^3 from k = 1 to k = n is equivalent to sum of k^3 from k = 1 to k = (n-1). So their difference = n^3.

2008-09-23 10:16:05 補充:
That is (1^3 + 2^3 + 3^3 +.......+ (n-1)^3 + n^3) - [ 0^3 + 1^3 + 2^3 + ......+ (n-1)^3] = n^3.


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