Note: Sorry for all these questions, got my finals in a few days.

The question

Starting with the geometric series for |z| < 1, simplify the following series for |z| < 1, (remember you can integrate or differentiate a power series term by term within its disc of convergence):

At first I thought I could pull the n out, and write it as , but it doesn't really make sense. Perhaps I'm just sleep deprived, but I'm having trouble getting this solved.

Any suggestions?