How do I know that the expression:

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

Is equal to the infinite sum:

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

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

Is equal to the infinite sum:

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