Electric Field Intensity at the Origin!

Using formula of field for a point charge $E=\dfrac{q}{4\pi\epsilon_0r^2}$ and Superposition principle , the net field by all the charges is :

$E_{net}=\dfrac{q}{4\pi\epsilon_0}\left(1+\dfrac1{2^2}+\dfrac{1}{4^2}+\dfrac{1}{8^2}\cdots\right)$

$=\dfrac{q}{4\pi\epsilon_0}\underbrace{\left(1+\dfrac1{2^2}+\dfrac{1}{2^4}+\dfrac{1}{2^6}\cdots\right)}_{\color{#D61F06}{\text{(Infinite GP)}}}$

$\large =\dfrac{q}{4\pi\epsilon_0}\left(\dfrac{1}{1-1/4}\right)$

$\large =\dfrac{q}{\color{#20A900}{3}\pi\epsilon_0}$

$\therefore\huge\Gamma (\color{#20A900}{3}+1)=\boxed 6$