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Re: Series Summation Question

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clashton <clashton@gmail.com> writes:

> I am a little curious about whether Maple can evaluate a certain
> infinite sum that fails with Mathematica (I do not have Maple so
> cannot test it myself).
>
> Here is the sum in Mathematica:
> Sum[q^(-6 + 4*n)/(1 - q^(-5 + 4*n)), {n, 0, Infinity}] /. {q -> 0.1}
> This leads to and error,
> but
> (Sum[q^(-6 + 4*n)/(1 - q^(-5 + 4*n)), {n, 0, 1}] /. {q -> 0.1)
>                                  +
> (Sum[q^(-6 + 4*n)/(1 - q^(-5 + 4*n)), {n, 2, Infinity}] /. {q -> 0.1})
> gives the correct answer, which I find a little strange.
>
> How does Maple perform on the original sum?

Summing numerically (and guessing at the meaning of the Mathematica):

(**) S := Sum(q^(-6 + 4*n)/(1 - q^(-5 + 4*n)), n=0..infinity);
                                  infinity
                                   -----      (-6 + 4 n)
                                    \        q
                             S :=    )     ---------------
                                    /           (-5 + 4 n)
                                   -----   1 - q
                                   n = 0

(**) evalf(eval(S,q=1/10));
                                     -21.10120010



-- 
Joe Riel

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Series Summation Question clashton <clashton@gmail.com> - 2012-01-25 22:46 -0800
  Re: Series Summation Question Axel Vogt <&noreply@axelvogt.de> - 2012-01-26 19:41 +0100
  Re: Series Summation Question Joe Riel <joer@san.rr.com> - 2012-01-26 08:21 -0800
    Re: Series Summation Question clashton <clashton@gmail.com> - 2012-01-26 16:45 -0800
      Re: Series Summation Question Peter Pein <petsie@dordos.net> - 2012-01-27 07:31 +0100
        Re: Series Summation Question Peter Pein <petsie@dordos.net> - 2012-01-27 07:55 +0100
          Re: Series Summation Question clashton <clashton@gmail.com> - 2012-01-28 07:59 -0800
          Re: Series Summation Question Axel Vogt <&noreply@axelvogt.de> - 2012-01-28 20:21 +0100
            Re: Series Summation Question Peter Pein <petsie@dordos.net> - 2012-02-02 12:21 +0100

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