Confirming a Summation Identity

1. May 9, 2013

eddybob123

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.

2. May 11, 2013

CompuChip

Looks like the proof is also on Wikipedia :)

3. May 11, 2013

eddybob123

So the formula in my first post is correct?