Which programming language or a library can process Infinite Series?

Question

Which programming language or a library is able to process infinite series (like geometric or harmonic)? It perhaps must have a database of some well-known series and automatica

Answer 1

Maxima can calculate some infinite sums, but in this particular case it doesn't seem to find the answer :-s

(%i1) sum((-1)^k/(2*k), k, 1, inf), simpsum;
                                 inf
                                 ====       k
                                 \     (- 1)
                                  >    ------
                                 /       k
                                 ====
                                 k = 1
(%o1)                            ------------
                                      2

but for example, those work:

(%i2) sum(1/(k^2), k, 1, inf), simpsum;
                                        2
                                     %pi
(%o2)                                ----
                                      6

(%i3) sum((1/2^k), k, 1, inf), simpsum;
(%o3)                                  1