Show that the series $\sum_{n=1}^{\infty} n^{q}x^{n}$ is absolutely convergent, and that $\lim_{n\to\infty} n^qx^n=0$.
Show that $\sum_{n = 1}^\infty n^qx^n$ is absolutely convergent, and that $\lim_{n \rightarrow \infty}$ $n^qx^n = 0$