Confirming a Summation Identityby eddybob123 Tags: bernoulli number, binomial, identity, power series, summation 

#1
May913, 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?:
$$\sum_{k=1}^nk^m=\frac{1}{m+1}\sum_{k=0}^{m}\binom{m+1}{k}B_k\;n^{mk+1}$$ where ##B_k## denotes the kth Bernoulli number. 



#2
May1113, 06:16 AM

Sci Advisor
HW Helper
P: 4,301

Looks like the proof is also on Wikipedia :)




#3
May1113, 02:18 PM

P: 115

So the formula in my first post is correct?



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