Michel Van den Bergh <michel.vandenbergh <at> uhasselt.be> writes:
> http://math.depaul.edu/~mash/telescopetams.pdf
>
> Regards,
> Michel
>
Thanks for the reference. It gives neccesary and sufficient conditions for a
rational function over the integer to be telescopic. The paper is very easy to
read, i think that even high school pupils can get the general ideas.
Perhaps i can improve ratsum to test cases in which the symbolic summation
gives a rational number, like in the paper.
Best regards.
Just for fun, you consider sum_n 1/(3n+1)^2 (*) and then sum_n
(1/(3n+1)^2+1/(3n+2)^2), the first one is sum_ an and the last one is
sum b_n with b_n = a_n + a_(n+1) so trivially sum bn = (2* sum a_n) - a_1.
-M