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    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 :|
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    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
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    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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