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  4. 1+(3/2)+(5/22)+(7/23)+ ldots ldots . upto ∞ is

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

KCETKCET 2022

Solution:

$S_{\infty}=\frac{a}{1-r}+\frac{d r}{(1-r)^{2}}=\frac{1}{1-\frac{1}{2}}+\frac{2\left(\frac{1}{2}\right)}{\frac{1}{4}}=2+4=6$