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 "MCQ" from 8. sequence and series→8. sequence and series — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $f:R \to R$ be such that $f(1)\, = 3$ and $f'\,(1) = 6$. Then $\mathop {\lim }\limits_{x \to 0} {\left\{ {\frac{{f(1 + x)}}{{f(1)}}} \right\}^{\frac{1}{x}}}$ equals

If $\mathrm{n} \in \mathrm{N}$, then $11^{\mathrm{n}+2}+12^{2 \mathrm{n}+1}$ is divisible by:

Probability is 0.45 that a dealer will sell at least 20 television sets during a day, and the probability is 0.74 that he will sell less that 24 televisions. The probability that he will sell 20, 21, 22 or 23 televisions during the day, is:

If $A + B + C = {180^o},$ then the value of $(\cot B + \cot C)$ $(\cot C + \cot A)\,\,(\cot A + \cot B)$ will be

The normal to the rectangular hyperbola $xy = c^2$ at the point $'t_1'$ meets the curve again at the point $'t_2'$ . Then the value of $t_{1}^{3} t_{2}$ is

If the line $y = mx$ bisects the angle between the lines $ax^2 + 2h xy + by^2 = 0$ then $m$ is a root of the quadratic equation :

If $P (2 , 8)$ is an interior point of a circle $x^2 + y^2 - 2x + 4y - p = 0$ which neither touches nor intersects the axes , then set for $p$ is

If the roots of the equation $a{x^2} + bx + c = 0$ are $l$ and $2l$, then

If $A$ and $B$ are the coefficients of ${x^n}$ in the expansions of ${(1 + x)^{2n}}$ and ${(1 + x)^{2n - 1}}$ respectively, then

The line $3x + 2y = 24$ meets $y$-axis at $A$ and $x$-axis at $B$. The perpendicular bisector of $AB$ meets the line through $(0, - 1)$ parallel to $x$-axis at $C$. The area of the triangle $ABC$ is ............... $\mathrm{sq. \, units}$