Solve for x if $1 + x + x^2 + x^3 .... = 2$ I've gone as far as rewriting it as
$$\sum_{n=1}^\infty x^{n-1} = 2$$
Not sure where to go from here.

$$|x|<1 \to \\1+x+x^2+x^3+x^4+...=2\\ 1+x(1+x+x^2+x^3+x^4+...)=2\\1+x(2)=2\\x=\frac{1}{2}$$
or 
$$\\1+x+x^2+x^3+x^4+...=2\\ 1+x+x^2(1+x+x^2+x^3+x^4+...)=2\\1+x+x^2(2)=2\\2x^2+x-1=0\\x=\frac{1}{2} \color{red}{\checkmark}\\x=-1 ,\color{red}{|x|<1}$$
so $x=-1 $ is not acceptable
