1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution This is not graded homework, but optional exercises I found in my textbook. It's days before my exam, but I'm still not sure how to do problems like this. I would really appreciate if someone can teach me how to solve this. For part a, I think we have to look at the partial sum, but how can we get the partial sum in the first place? For part b, should we use the Weierstrass M-test? Is it true that to prove that a SERIES of functions is uniformly convergent, most of the time we're going to use the Weierstrass M-test? Is this the only way? Thanks a lot!