number theory

plzhelpme

hi everybody, I have a question in math to figure out the general term for the sum of the pth powers of n integers. I found a formula called faulhabers formula to do this question, but I do not understand the method behind it. can someone please help me?

shmoe

You can prove it using Euler-MacLaurin summation, where you essentially rewrite the sum as a Stieltjes integral then integrate by parts enough time that the remaining integrand is zero (the p+1 derivitative of x^p vanishes). Look up Euler-MacLaurin summation (lot's of references).

Or are you trying to understand how to apply Faulhaber's in a given situation? It's just plug and chug, but you'll need to know what the Bernoulli numbers are (again, lots of references)