Explanation

(b) The schematic diagram of distribution of charges on $x -$axis is shown in figure below:
Total force acting on $1C$ charge is given by
$F = \frac{1}{4\pi\varepsilon_{0}}\left\lbrack \frac{1 \times 1 \times 10^{- 6}}{(1)^{2}} + \frac{1 \times 1 \times 10^{- 6}}{(2)^{2}} \right.\ $
$\left. \ + \frac{1 \times 1 \times 10^{- 6}}{(4)^{2}} + \frac{1 \times 1 \times 10^{- 6}}{(8)^{2}} + \ ....\infty \right\rbrack$
$= \frac{10^{- 6}}{4\pi\varepsilon_{0}}\left( \frac{1}{1} + \frac{1}{4} + \frac{1}{16} + \frac{1}{64} + \ldots\infty \right) = 9 \times 10^{9} \times 10^{- 6}\ \left( \frac{1}{1 - \frac{1}{4}} \right)$
$= 9 \times 10^{9} \times 10^{- 6} \times \frac{4}{3} = 9 \times \frac{4}{3} \times 10^{3} = 12000\ N$