My question is a bit more general... I'm in calculus 2 now working through the chapter on finding whether or not a series converges. Many of the tests don't even tell you what a series converges to, just the fact that it does (or doesn't). It's neat and all, but I'm curious, is there a point to this?

Back in algebra, we learned how to do fraction decomposition. It's neat and all, but seemed mostly pointless. It wasn't until Calculus 2 that I realized fraction decomposition is extremely important in taking integrals of a lot of different functions, which in turn is useful for finding areas under curves or in rotated curves. I'm just wondering if this series convergence/divergence has some sort of future importance or not.