$1 + \frac{3}{2} + \frac{5}{2^{2}} + \frac{7}{2^{3}}\ldots.\infty$ is equal to

Question

Dr. Abubacker · Accepted Answer

(d)
This progression is an arithmetico-geometric series.
$	herefore\ S_{\infty} = \frac{a}{1 - r} + \frac{dr}{(1 - r)^{2}}$
$= \frac{1}{1 - 1/2} + \frac{2}{(1 - 1/2)^{2}}$
$= \ \frac{2}{1/2} + \frac{2}{1/4}$
$= 4 + 8 = 12$

Q. $1 + \frac{3}{2} + \frac{5}{2^{2}} + \frac{7}{2^{3}}\ldots.\infty$ is equal to

Explanation

Reviewed by Dr. Abubacker

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