The magnitude of gravitational field intensity at point O will be the sum of gravitational field intensity due to each mass m

$I=Gm\bigg[\large\frac{1}{r^2}+\frac{1}{(2r)^2}+\large\frac{1}{(4r^2)}....\bigg]$

$\quad=\large\frac{Gm}{r^2}$$\bigg[1+\large\frac{1}{2^2}+\frac{1}{4^2}+\large\frac{1}{8^2}....\bigg]$

$\quad=\large\frac{Gm}{r^2}\bigg[\large\frac{1}{1-\Large\frac{1}{2^2}}\bigg]$

$\quad=\large\frac{Gm}{r^2}\bigg[\large\frac{1}{1-\Large\frac{1}{4}}\bigg]$

$\quad=\large\frac{4Gm}{3r^2} $

Hence b is the correct answer.