$\frac{1}{1-x}$ series expansion

How do I know that the expression:

$$\frac{1}{1-x}$$

Is equal to the infinite sum:

$$-\left(\frac{1}{x}\right)-\left(\frac{1}{x}\right)^2-\left(\frac{1}{x}\right)^3-\left(\frac{1}{x}\right)^4+...$$

Thanks!

-

If $|x^{-1}|<1$ then the sum of geometric series: $$-\sum_{n=1}^\infty x^{-n}=-\frac{1}{x}\frac{1}{1-x^{-1}}=\frac{1}{1-x}$$
Hint: If I were you, I would try to divide $1$ by $1-x$. This is an elementary way to find those terms.