Evaluating nested radicals

Calculus Level 1

$\sqrt{ \frac{2}{2^{2^0}} + \sqrt{ \frac{2}{2^{2^1}} + \sqrt{ \frac{2}{2^{2^2}} + \sqrt{ \frac{2}{2^{2^3}} +\cdots }}}}$

If the value of above expression is in the form $\sqrt{A}$ , find the value of $A$ .