Prove the following identities
(n)+2(n)+3(n)+......+n(n)=n x 2^(n-1)
_1___2____3_______n
好似(n) =n!/k!(n-k)!
_____k
數學 Binomial theorem
2009-09-30 6:36 am
回答 (1)
2009-09-30 6:59 am
✔ 最佳答案
Consider (1 + x)n = nC0 + nC1x + nC2x2 + ... + nCnxnDifferentiate both sides with respect to x
n(1 + x)n-1 = nC1 + 2nC2x + ... + nnCnxn-1
Put x = 1
nC1 + 2nC2 + ... + nnCn = n X 2n-1
參考: Physics king
收錄日期: 2021-04-19 15:58:28
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