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

MCQ

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

A
$1$
B
$5$
✓
$9$
D
$10$

✓

Answer

Correct option: C.

$9$

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 $

$\Rightarrow \boxed{d = 9}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The ratio of the sums of first $n$ even numbers and $n$ odd numbers will be

If $y = {{a + b{x^{3/2}}} \over {{x^{5/4}}}}$ and $y' = 0$ at $x = 5$, then the ratio $a:b$ is equal to

The value of $\frac{{\tan {{70}^o} - \tan {{20}^o}}}{{\tan {{50}^o}}} = $

The sum of all the natural numbers for which $log_{(4-x)}(x^2 -14x + 45)$ is defined is -

If $f(x) = \frac{1}{{\sqrt {x + 2\sqrt {2x - 4} } }} + \frac{1}{{\sqrt {x - 2\sqrt {2x - 4} } }}$ for $x > 2$, then $f(11) = $

If $A$ is a symmetric matrix, then matrix $M'AM$is

The roots of the equation ${x^4} - 4{x^3} + 6{x^2} - 4x + 1 = 0$ are

A particle $P$ starts from the point $z_0=1+2 i$, where $i=\sqrt{-1}$. It moves first horizontally away from origin by $5$ units and then vertically away from origin by $3$ units to reach a point $z_1$. From $z_1$ the particle moves $\sqrt{2}$ units in the direction of the vector $\hat{\mathrm{i}}+\hat{\mathrm{j}}$ and then it moves through an angle $\frac{\pi}{2}$ in anticlockwise direction on a circle with centre at origin, to reach a point $z_2$. The point $z_2$ is given by

$\int_{}^{} {\sqrt {{x^2} - 8x + 7} } \;dx = $

If $\int_0^1 {{e^{{x^2}}}(x - \alpha )\,dx = 0,} $ then