1210

I need to know step-by-step solution how to get the formula (on the right) from this sum of infinite sequence (on the right).



can anyone help me? thank you all very much in advance.

CRGreathouse

I don't think you mean infinite -- the sum only runs to n. If it was infinite you'd be looking at zeta(-4) which is a trivial zero by analytic continuation.

You can solve this by induction. Show that it works for n = 1, and that if it holds for n it also holds for n+1. Do this by adding

n(n+1)(2n+1)(3n^2+3n-1)/30+(n+1)^4

and simplifying.

1210

thank you very much! yes, youre right this is not an infinite seqeunce, im sorry, but can you give me just one more advise how you came to this?

thanks.

CRGreathouse

Expand the formula I gave you, then re-collect terms so the final formula is (n+1)(n+2)(2(n+1)+1)(3(n+1)^2+3(n+1)-1)/30.