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Re: Approximating the sum of a series

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On 7/23/2013 2:48 AM, mmatica@personal.ro wrote:
> I want to compute
> evalf(s(0,infinity));
>
> where
> s:=(a,b)->Sum(exp(-n^2/10000),n=a..b);
>
> and Maple refuses. It (probably) declares the series divergent.
> Maple accepts to approximate s(1000,infinity).
> It is < 10^(-42) so, s(0,1000) gives the answer but
> the question is: how could Maple be convinced to compute directly
> evalf(s(0,infinity))?
>
>

one way to handle these problem is to do the sum
for say k, and then take the limit of the result as
k -> infinity.

That normally works better, but when I tried this method,
it also did not work here.

But a plot shows the sum converges to 89.122, so
it convergent.

--Nasser

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Approximating the sum of a series mmatica@personal.ro - 2013-07-23 00:48 -0700
  Re: Approximating the sum of a series "Nasser M. Abbasi" <nma@12000.org> - 2013-07-23 07:17 -0500
  Re: Approximating the sum of a series acer <maple@rogers.com> - 2013-07-23 07:01 -0700
    Re: Approximating the sum of a series Axel Vogt <&noreply@axelvogt.de> - 2013-07-23 18:57 +0200
  Re: Approximating the sum of a series mmatica@personal.ro - 2013-07-23 12:13 -0700
  Re: Approximating the sum of a series mmatica@personal.ro - 2013-07-23 12:29 -0700
    Re: Approximating the sum of a series Axel Vogt <&noreply@axelvogt.de> - 2013-07-23 22:11 +0200
      Re: Approximating the sum of a series mmatica@personal.ro - 2013-07-23 14:08 -0700
        Re: Approximating the sum of a series Axel Vogt <&noreply@axelvogt.de> - 2013-07-28 19:40 +0200
        Re: Approximating the sum of a series / an Integral Axel Vogt <&noreply@axelvogt.de> - 2013-07-29 22:22 +0200
          Re: Approximating the sum of a series / an Integral Herman Rubin <hrubin@skew.stat.purdue.edu> - 2013-07-30 18:03 +0000
      Re: Approximating the sum of a series Herman Rubin <hrubin@skew.stat.purdue.edu> - 2013-07-25 23:37 +0000
    Re: Approximating the sum of a series acer <maple@rogers.com> - 2013-07-23 14:02 -0700

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