Confirming a Summation Identity


by eddybob123
Tags: bernoulli number, binomial, identity, power series, summation
eddybob123
eddybob123 is offline
#1
May9-13, 06:24 PM
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.
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CompuChip
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#2
May11-13, 06:16 AM
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P: 4,301
Looks like the proof is also on Wikipedia :)
eddybob123
eddybob123 is offline
#3
May11-13, 02:18 PM
P: 115
So the formula in my first post is correct?


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