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Math Help - finding the series

  1. #1
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    finding the series

    How do we calculate for a given n and k the value of S_n=T_n+U_n where T_n=1^k+2^k+3^k+..n^k and U_n= 1^1+2^2+3^3+..n^n
    Is this some kind of series/is there any general formula to it ?
    Thanks.
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  2. #2
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    Re: finding the series

    Quote Originally Posted by pranay View Post
    How do we calculate for a given n and k the value of S_n=T_n+U_n where T_n=1^k+2^k+3^k+..n^k and U_n= 1^1+2^2+3^3+..n^n
    Is this some kind of series/is there any general formula to it ?
    It is true that S_n  = \sum\limits_{j = 1}^n {\left( {j^k  + j^j } \right)} .

    But is that really what you are asking?
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  3. #3
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    Re: finding the series

    actually i intend to find S_n +S_{n-1}-2S_{n-2}
    Last edited by pranay; September 5th 2011 at 09:34 AM. Reason: correction
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