Confirming a Summation Identity

  1. 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. jcsd
  3. CompuChip

    CompuChip 4,297
    Science Advisor
    Homework Helper

    Looks like the proof is also on Wikipedia :)
     
  4. So the formula in my first post is correct?
     
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