Limit under Evaluation

Calculus Level 3

$\displaystyle \lim_{n \to \infty} \left( (1+x)(1+x^2)(1+x^4)....(1+x^{2^n}) \right)=?$

provided that $|x|<1$ .

\dfrac{x^2}{1-x}

\dfrac{x}{1-x}

None of the given. Doesn't exist.

\dfrac{1}{1-x}