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
Just install sympy on your computer. Then do the following code:
from sympy.abc import i, k, m, n, x from sympy import Sum, factorial, oo, IndexedBase, Function Sum((-1)**k/(2*k+1), (k, 0, oo)).doit()
Result will be: pi/4