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

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Correct option is D

This progression is an arithmetico-geometric series.∴ S∞=a1−r+dr(1−r)2=11−1/2+2(1−1/2)2=21/2+21/4=4+8=12

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1+32+522+723…∞ is equal to

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