|Dec4-05, 04:50 PM||#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?
|Dec5-05, 09:40 AM||#2|
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)
|Similar Threads for: number theory|
|Number Theory: Calculating mod large number||Calculus & Beyond Homework||9|
|Number Theory?||Linear & Abstract Algebra||6|
|measure theory and number theory?||Linear & Abstract Algebra||18|
|number theory help||Calculus & Beyond Homework||5|
|Division theory..and Prime Number theory..||Linear & Abstract Algebra||3|