If 3 + 1 4 (3 + d) + 1 4^2 (3 + 2d) + ....... = 8 then value of d… - Vidyadip

Question

If $3 + \frac{1}{4} (3 + d) + \frac{1}{4^2} (3 + 2d) + .......\infty = 8$ then value of $d$ is :-

✓

Answer

c
$S=3+\frac{3+d}{4}+\frac{3+2 d}{4^{2}}+\ldots \ldots+\infty$ ........$(1)$

$\frac{S}{4}=\frac{3}{4}+\frac{3+2 d}{4^{2}}+\ldots \ldots+\infty$ ..........$(2)$

$\frac{3 S}{4}=3+\frac{d}{4}+\frac{d}{4^{2}}+\ldots \ldots+\infty$

$S=\frac{4(9+d)}{9}=8 $

$\Rightarrow \boxed{d = 9}$

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