1. The problem statement, all variables and given/known data I need to fin the sum of the following two infinite series: 1. Ʃ[n=0 to ∞] ((2^n + 3^n)/6^n) and 2. Ʃ[n=2 to ∞] (2^n + (3^n / n^2)) (1/3^n) 2. Relevant equations use the sum Ʃ[n=2 to ∞] (1/n^2) = ∏^2 / 6 as necessary 3. The attempt at a solution I tried to manipulate them both to make them geometric or telescoping, to no avail. It seems like neither series is telescoping or geometric, so isn't it impossible to definitively sum them? I started to sum them by adding their partial sums, but they converge very slowly and it would take hundreds of calculations to provide enough evidence for the sums.