# Confirming a Summation Identity

by eddybob123
Tags: bernoulli number, binomial, identity, power series, summation
 P: 115 Hi all, I found this "identity" online on Wikipedia, and realized that it would actually come in pretty useful for me, if only I could prove that it is true. Can you guys help me on that?: $$\sum_{k=1}^nk^m=\frac{1}{m+1}\sum_{k=0}^{m}\binom{m+1}{k}B_k\;n^{m-k+1}$$ where ##B_k## denotes the kth Bernoulli number.
 Sci Advisor HW Helper P: 4,301 Looks like the proof is also on Wikipedia :)
 P: 115 So the formula in my first post is correct?

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