An infinite number of charges each of magnitude \(q\) are placed on the \(x\)-\(\text {axis}\) at the distance of \(1,2,4,8,16,\ldots\) \(\text{m}\) respectively. Find the intensity of electric field at the origin.

If the intensity can be expressed in the form \(\dfrac { q }{ n\pi { \varepsilon }_{ o } }\), find \(\Gamma (n+1)\).

Assume the medium to be vacuum.

Here, \(\Gamma (n)\) and \({ \varepsilon }_{ o }\) represent the Gamma function and permittivity of free space respectively.

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