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Number theory 
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#1
Dec405, 04:50 PM

P: 1

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?



#2
Dec505, 09:40 AM

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P: 1,995

You can prove it using EulerMacLaurin 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 EulerMacLaurin 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) 


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