Figure shows a system of point masses placed on X-axis. Find the net gravitational field intensity at the origin

Take sum of an infinite GP as `S = (a)/(1-r)`
where a= first term and r = Least common ratio.

Explanation

Net gravitational field intensity at the origin,
`E_("net")=E_(1)+E_(2)+E_(3)+E_(4)+....infty` terms
`=(GM)/((1)^(2))hat(i)+(GM)/((2)^(2))hat(i)+(GM)/((4)^(2))hat(i)+.....infty` terms
`=GM hat(i)(1+(1)/(4)+(1)/(16)+....infty)" "("Here", a=1 and r=(1)/(4))`
So, `E_("net")=GM((a)/(1-r))hat(i)=GM hat(i)((1)/(1-1//4))=GMhat(i)((1)/(3//4))`
`rArr E_("net") =(4)/(3)GM hat(i)`.