An infinite number of charges of equal magnitude q, but of opposite sign are pla

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An infinite number of charges of equal magnitude q, but of opposite sign are placed alternately starting with positive charge along x- axis at x = 1 m; x = 2 m,x = 4 m, x= 8 m and so on. The electric potential at the point x = 0 due to these charges will be (in S.I units and k =

\frac{1}{4 π ϵ_{0}}

Options:

A . kq2

B . kq3

C . k2q3

D . k3q2

Answer: Option C
:
C

V = V_{1} + V_{2} + V_{3} + . . . . . . . = \frac{1}{4 π ϵ_{0}} [\frac{q_{1}}{r_{1}} - \frac{q_{2}}{r_{2}} + \frac{q_{3}}{r_{3}} - \frac{q_{4}}{r_{4}} + . . . . . . .] = k [\frac{q}{1} - \frac{q}{2} + \frac{q}{4} - \frac{q}{8} + . . . . . .] = k q [1 - \frac{1}{2} + \frac{1}{2^{2}} - \frac{1}{2^{3}} + . . . . . .] = k q [\frac{1}{1 + \frac{1}{2}}] = \frac{2 k q}{3}

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