Question

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Answer 1

Field = GM/x^2 = G/x^2 (since M = 1 kg)
Now,

Force = mass*Field = 3( Field due to first particle + field due to second particle + ....... + field due to infinite particle)

= 3G ( 1/1^2 + 1/2^2 + 1/4^2 + 1/8^2 + .... + infinity)
= 3G ( 1+1/4+1/16+1/64+.......)
Applying the formula for infinite geometric progression,
For any given geometric progression like a,ar,ar^2,..... infinity
where r<1
Sum of infinite terms = a/1-r
Here, a = 1 and r = 1/4
Therefore,

= 3G ( 1/1-1/4) = 3G * 1/3/4 = 3G * 4/3 = 4 G

Therefore, the total force on the particle will be 4G Newton.