I am confused about how to find a sum of a power series, especially when it contains factorials and I can't quite get it to look like a geometric series. Is it the same thing as finding a limit (and then I would follow the various tests for convergence of the different kinds of series)? Is it the same thing as finding an "exact value" (which I think means finding a function in terms of x)?
I can't give the exact problems I am working with because it is a take home test, but I hope if I make up an example, this will work for my general questions about the concept:
The Attempt at a Solution
With one problem similar to above I am working with, when I did the ratio test it appears to converge to zero; does that mean the sum equals zero?