Geometric Summation Question $\sum_{n=2}^{\infty} n(n-1)x^{(n-2)} = \frac{2}{(1-x)^3}$

Question

My Prof wrote that

$\sum_{n=2}^{\infty} n(n-1)x^{(n-2)} = \frac{2}{(1-x)^3}$

when $-1< x<1$

I do not understand where the above formula comes from. Can someone please explain the steps or provide a hint?

Thanks!

Answer 1

Start with the formula $\sum_{n=0}^\infty x^n=\frac{1}{1-x}$. Then take two derivatives.