calculus - Evaluating $sum_{n=1}^{infty}frac{n}{16^n}$

I'm trying to evaluate the sum of the following infinite series:

$$\sum_{n=1}^{\infty}\frac{n}{16^n}$$

I know it converges to $\frac{16}{225}$, but I don't know how to reach this solution. It's not a geometric series or a telescoping sum, and I haven't found any way to relate it to a Taylor or Maclaurin series. How should I approach this problem?

Answer

Hint:

What is the derivative of $\;\sum_{n=1}^{\infty} x^n$?