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September 19th, 2007, 05:45 AM  #1 
Newbie Joined: Sep 2007 Posts: 17 Thanks: 0  help with the calculus of infinite sequence
I need to know stepbystep 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. 
September 19th, 2007, 11:03 AM  #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+3n1)/30+(n+1)^4 and simplifying. 
September 19th, 2007, 10:44 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:
 
September 20th, 2007, 08:06 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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calculus, infinite, sequence 
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