1. The problem statement, all variables and given/known data 3. The attempt at a solution I really couldn't figure this one out. It's definitely not telescoping series because I don't see repeating terms that cancel. I would try to compare it to a geometric series. so what I did was factoring out a 4^n: 4^n(2+sinn-(1/2+sinn)) replacing (2+sinn-(1/2+sinn)) with "a" Then I noticed the bounds 1<2+sinn<3 so the whole thing inside the bracket is oscillating between 0<a<8/3 So i concluded that the series is divergent? (highly unsure) because the coefficient that 4^n multiplies by (by coefficient I mean "a") is always either 0 or a positive number. So when it is 0, there will be no effect. When it is a positive number, the sums will add up, and the series will eventually go to infinity.. Eh.. is that.. a valid line of reasoning? Thanks in advance, Lilly.