sums



On Friday 07 November 2008 23:50 you wrote:
> Dear Alexey,
>
> Thank you very much for your help to calculate the sum s1 :
>
> ...
>
> In the same way I tried to calculate the sum s2:
>
> 4/3+simplify_sum(sum((-1/(2*k)+1/(2*2*k+1)+1/(2*2*k+3)),k,1,inf));
>
> but the answer was always  -inf +4/3  instead of  3*log(2)/2 ?
>
> Perhaps there exists an other ,more sophisticated, way to calculate
> s2 ?

Looks like a bug in simplify_sum.

  (%i1) load ("simplify_sum")$

  (%i2) kth_term : -1/(2*k)+1/(2*2*k+1)+1/(2*2*k+3)$

  (%i3) simplify_sum(sum(kth_term,k,1,inf));
  (%o3) inf

However, it gives the right answer for the ratsimp'ed term.

  (%i4) simplify_sum(sum(ratsimp(kth_term),k,1,inf));
  (%o4) -(-3*log(2)+%pi/2-%gamma+4/3)/4-(-3*log(2)-%pi/2-%gamma+4)/4-%gamma/2

  (%i5) ratsimp(4/3+%);
  (%o5) 3*log(2)/2

-- 
Sweetmorn, Aftermath 19 YOLD 3174
Alexey Beshenov  http://beshenov.ru/