what is the diagram for this???

Solution:
Charges, $q_1, q_2, q_3.......\infty$ are placed on a straight line at distance, $\sqrt{2}, \sqrt{4}, \sqrt{8},\sqrt{16},.......\infty$ from a charge Q at the origin.


Here, $Q=q_1=q_2=q_3.......=q_n...=1 \mathrm{C} \left(\mathrm{given}\right)$

​​​​​​So, net force acting on the first charge Q,

$$\begin{gathered} F_{resul\tan t}=\frac{1\times 1}{4\pi {\epsilon }_{\circ }}\left[\frac{1}{{\left(\sqrt{2}\right)}^2}+\frac{1}{{\left(\sqrt{4}\right)}^2}+\frac{1}{{\left(\sqrt{8}\right)}^2}+\frac{1}{{\left(\sqrt{16}\right)}^2}........\infty \right] \\ =9\times {10}^9\times \left[\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}..........\infty \right] \\ =9\times {10}^9\times \left[\frac{1}{2}+{\left(\frac{1}{2}\right)}^2+{\left(\frac{1}{2}\right)}^3+{\left(\frac{1}{2}\right)}^4..........\infty \right] .....\left(1\right) \\ \mathrm{To}, \mathrm{solve} \mathrm{this} \mathrm{we} \mathrm{can} \mathrm{use} \mathrm{the} \mathrm{sum} \mathrm{of} \mathrm{infinite} \mathrm{geometric} \mathrm{progration}: \\ \mathrm{first} \mathrm{term}, a=\frac{1}{2} \\ \mathrm{common} \mathrm{ratio}, r = \frac{1}{2}<1 \\ {S}_{\infty }=\frac{a}{1-r} \\ \Rightarrow \frac{1}{2}+{\left(\frac{1}{2}\right)}^2+{\left(\frac{1}{2}\right)}^3+{\left(\frac{1}{2}\right)}^4..........\infty =\frac{\left({\displaystyle \frac{1}{2}}\right)}{\left(1-\frac{1}{2}\right)}=1 \\ \mathrm{So}, F_{resul\tan t}=9\times {10}^9\times \left[\frac{1}{2}+{\left(\frac{1}{2}\right)}^2+{\left(\frac{1}{2}\right)}^3+{\left(\frac{1}{2}\right)}^4..........\infty \right] \\ =9\times {10}^9\times 1 \\ =9\times {10}^9 \mathrm{N} \end{gathered}$$



Hence, the correct answer is option (a).