1. The problem statement, all variables and given/known data Find the range of uniform convergence for the following series η(x) = ∑(-1)n-1/nx ζ(x) = ∑1/nx with n ranging from n=1 to n=∞ for both 2. Relevant equations To be honest I'm stumped with where to begin altogether. In my text, I'm given the criteria for uniform convergence, which is given by |S(x) - sn(x)| < ε for all n ≥ N, and I know that S(x) is defined as S(x) = lim n→∞ sn(x). 3. The attempt at a solution I sort of intuitively grasp what the equations are saying, which is if all the terms cluster together for a large enough n, then the series is said to be uniformly convergent. I am just unsure of how to actually test the given series to see if they meet this criteria, or how to go about assigning values to the criteria listed as the above equations. Any help would be greatly, greatly appreciated, thanks!!