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.
Ok, fair enough. I'm just not sure that finding the sum of an infinite series is really helpful outside of in a purely academic environment, but I've been very wrong before, so was just wondering if more advanced math made greater use of this idea than I was aware of. It doesn't really matter... I need to learn this to get to Calculus 3 if nothing else. For some reason it's a lot more interesting to me if there are other, more concrete applications.