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Math Help - FInding the sum

  1. #1
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    FInding the sum

    Hi, how can one find the sum of the series:
    for the sequence such that:

    Is it some series?
    Thanks.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: FInding the sum

    Quote Originally Posted by pranay View Post
    Hi, how can one find the sum of the series:
    for the sequence such that:

    Is it some series?
    Thanks.
    I don't fully understand your question, but maybe this would be helpful.

    S_n(x)=\sum^n_{k=1}a_kx^k

    S_n is clearly S_n(1).

    Now, the derivative of S_n(x) is:

    (S_n(x))'=(\sum^n_{k=1}a_kx^k)'=\sum^n_{k=1}ka_kx^  {k-1}.

    So (S_n(1))'=\sum^n_{k=1}ka_k .
    Last edited by Also sprach Zarathustra; July 19th 2011 at 12:22 PM.
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  3. #3
    Super Member girdav's Avatar
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    Re: FInding the sum

    You can find a_{n+1} writing (n+1)a_{n+1} = \sum_{k=1}^{n+1}ka_k -\sum_{k=1}^nka_k.
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  4. #4
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    Re: FInding the sum

    the value of S(2) and S(5) is
    0.70833333333 and
    0.73809523810 respectively . So how can one relate to calculating the differentiation?
    Thanks.
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