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Math Help - INDUCTION PROBLEM

  1. #1
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    Unhappy INDUCTION PROBLEM

    I have a question.This one's either really hard or really stupid


    it's an induction problem.
     (1 - 1/2^2) * (1- 1/3^2) * ....... * ( 1 - 1/n^2)  = (n+1)/2n


    been solving it since past several hours. but i am not getting my L.H.S = RH.S for this one.
    I started with proving if p(n) then p(n+10

    so L.H.S = [1 - 1/(n+1)^2] + (n+1)/2n

    R.H.s = (n+2)/2(n+1).

    I can't just prove them equal.

    Please help,
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  2. #2
    Eater of Worlds
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    Multiply instead of adding.

    Note that \frac{(n+1)}{2n}\cdot \left(1-\frac{1}{(n+1)^{2}}\right)=\frac{n+2}{2(n+1)}

    Which it what you want to show.
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  3. #3
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    I think it will be multiplied though.If you take out a term from summation you know that it needs to be added to the sum of all the other terms.
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  4. #4
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    oh well,i didn't see that..thanks!
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