What a series converges to?

for math (calculus), i'm curious if there are any ways to find what an infinite or finite series converges to. i'm wondering if such a way exists. and i don't mean just for geometric series, i mean for any converging series, like what does the series of 1/n^2 converge to? if anyone knows of a way that calculators or computers do it, then that will help to, but i don't just want an approximation method like adding the first ten members of the series, i would like a absolute formula. thanks.