# Dominated 2! Its Algebra cum Geometry

Calculus Level 3

$\sqrt{\frac{1}{2}}\times \sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}}\times \sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}}}\times \cdots = \dfrac{a}{b\pi }$

The equation above holds true for coprime positive integers $$a$$ and $$b$$, find the value of $$a^2 + 3b$$.

×