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September 19th, 2007, 06:45 AM | #1 |
Newbie Joined: Sep 2007 Posts: 17 Thanks: 0 | help with the calculus of infinite sequence
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. |
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September 19th, 2007, 12:03 PM | #2 |
Global Moderator Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms |
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. |
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September 19th, 2007, 11:44 PM | #3 | |
Newbie Joined: Sep 2007 Posts: 17 Thanks: 0 |
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? Quote:
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September 20th, 2007, 09:06 AM | #4 | |
Global Moderator Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms | Quote:
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