The problem says, "Write down the Taylor series of $\displaystyle Cos(x)$ about $\displaystyle x=0$ and sum the series $\displaystyle \sum_{0}^{inf} (-\pi ^2)^n / (2n)! 9^n$"

First question is, when do you stop writing terms of the series if it doesn't tell you?

Also, what does the second series have to do with the first one? This seems like two totally different problems crammed into one. Am I wrong?