If y = x + x^2 + x^3 + ....... , , , then , ,x = - Vidyadip

MCQ

If $y = x + {x^2} + {x^3} + .......\,\infty ,\,{\rm{then}}\,\,x = $

✓
$\frac{y}{{1 + y}}$
B
$\frac{{1 - y}}{y}$
C
$\frac{y}{{1 - y}}$
D
None of these

✓

Answer

Correct option: A.

$\frac{y}{{1 + y}}$

a
(a) $y = \frac{x}{{1 - x}}$(Infinite $G.P.$)

$\therefore y - yx = x$ or $y = x\,(1 + y)$

$i.e.$, $x = \frac{y}{{1 + y}}$.

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

More "M.C.Q (1 Marks)" from STD 11 - 8. sequence and series→STD 11 - 8. sequence and series — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The number of matrices of order $3 \times 3$, whose entries are either $0$ or $1$ and the sum of all the entries is a prime number, is$....$

If $ABCD$ is a cyclic quadrilateral, then the value of $\cos A - \cos B + \cos C - \cos D = $

The attendance of a class of $45$ boys for $10$ days is given as $40, 30, 35, 45, 44, 41, 38, 44$ and $41$ then the mean attendance of a class is:

If vertices of a parallelogram are respectively $(0, 0)$, $(1, 0)$, $(2, 2)$ and $(1, 2)$, then angle between diagonals is

Let $'E'$ be the ellipse $\frac{{{x^2}}}{9}$$+$$\frac{{{y^2}}}{4}$ $= 1$ $\& $ $'C' $ be the circle $x^2 + y^2 = 9.$ Let $P$ $\&$ $Q$ be the points $(1 , 2) $ and $(2, 1)$ respectively. Then :

All the five digits numbers in which each successive digit exceeds its predecessor are arranged in the increasing order of their magnitude. The $97^{th}$ number in the list does not contain the digit:

If ${m^{th}}$ terms of the series $63 + 65 + 67 + 69 + .........$ and $3 + 10 + 17 + 24 + ......$ be equal, then $m = $

If the equations $\text{x}^2+2\text{x}+3=0 $ and $\text{ax}^2+\text{bx}+\text{c}=0,\text{abc}\in\text{R},$ I have a common root, then $a : b : c$ is.

The number of solutions that the equation $sin5\theta cos3\theta = sin9\theta cos7\theta $ has in $\left[ {0,\frac{\pi }{4}} \right]$ is

$PQ$ is a double ordinate of the parabola ${y^2} = 4ax$. The locus of the points of trisection of $PQ$ is