[Maxima] Symbolic summation (was: levin versus ratsum)

[Michel Van den Bergh]

I noticed that GosperSum can easily do telescoping sums.

load(zeilberger);

limit(GosperSum(1/(k*(k+1)),k,1,n),n,inf);

Result:      1

Of course this does not work for sum(1/(3*k+1)^2+1/(3*k+2)^2,k,0,inf)
which is 8/9*zeta(2)=4/27*%pi^2.

Michel