# [Maxima] sums

Andrej Vodopivec andrej.vodopivec at gmail.com
Sat Nov 8 03:24:44 CST 2008

```On Fri, Nov 7, 2008 at 10:16 PM, Alexey Beshenov <al at beshenov.ru> wrote:
> 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.
>
>
>  (%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

I think you have an old version of simplify_sum. With maxima from cvs I get

(%i1) kth_term : -1/(2*k)+1/(2*2*k+1)+1/(2*2*k+3)\$
(%i2) simplify_sum(sum(kth_term,k,1,inf));
(%o2) (9*log(2)-8)/6

which is correct.

--
Andrej
```