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# Math questions for the gifted ones!!! watch

1. Hello my fellow mathematicians

I was wondering if you all could help me out with a problem O_O...well 2 really xD

1.) let S(N) = sigma (with 'N' on top and 'n=1' on the bottom) (-1)^(n-1) * n^3

Find S(2N) in terms of N, simplifying your answer as far as possible.

Hence write down an expression for S(2N+1) and find the limit, as N -> (infinity), of [S(2N+1) / N^3]

2.) It is given that I(n) = integral (boundaries of 1 and 0) (1+x^3)^(-n) dx where n>0

Show that:
d/dx[x(1+x^3)^(-n)] = -(3n-1)(1+x^3)^(-n) + 3n(1+x^3)^(-n-1) and hence or otherwise show that...

I(n+1) = 2^(-n)/(3n) + (1+ (1/(3n))I(n)

Thank you soo much guys ...I would like detailed working as to how you guys arrived at your answer because I really need to know :|
2. I've been looking all over the internet as to how to solve these questions but I'm not getting any luck...so can you guys please help
3. That's not how it works around here, you must first show your working so we can try to nudge you in the right direction with subtle hints.

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Updated: September 29, 2011
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