sequences and series - Why is $sum_{n=0}^{infty }left ( frac{1}{2} right )^{n}= 2$?

I'm sorry if this is duplicated, but I can not find any answer to it.

Answer

the geometric series for $|x|<1$

$$1+x+x^2+x^3+....=\frac{1}{1-x}$$
use $x=0.5$
$$1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...=\frac{1}{1-\frac{1}{2}}=2$$