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Math Help - Prove :

  1. #1
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    Prove :

    Show that for any natural number the sum

    1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\ldots + \frac{1}{n^2}

    lies between the values

    \left(1-\frac{2}{n+1}\right)\left(1-\frac{2}{2n+1}\right)\frac{\pi^2}{6} and \left(1-\frac{1}{2n+1}\right)\left(1+\frac{1}{2n+1}\right)  \frac{\pi^2}{6}.
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  2. #2
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    To start this, would one have to find the domain of the these two expressions over the natural numbers?


    and



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  3. #3
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    Quote Originally Posted by newtoinequality View Post
    Show that for any natural number the sum

    1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\ldots + \frac{1}{n^2}

    lies between the values

    \left(1-\frac{2}{n+1}\right)\left(1-\frac{2}{2n+1}\right)\frac{\pi^2}{6} and \left(1-\frac{1}{2n+1}\right)\left(1+\frac{1}{2n+1}\right)  \frac{\pi^2}{6}.
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