If $y = x - {x^2} + {x^3} - {x^4} + ......\infty $, then value of $x$ will be
$y + \frac{1}{y}$
$\frac{y}{{1 + y}}$
$y - \frac{1}{y}$
$\frac{y}{{1 - y}}$
If the sum of an infinite $G.P.$ and the sum of square of its terms is $3$, then the common ratio of the first series is
$0.14189189189….$ can be expressed as a rational number
If $1 + \cos \alpha + {\cos ^2}\alpha + .......\,\infty = 2 - \sqrt {2,} $ then $\alpha ,$ $(0 < \alpha < \pi )$ is
The sum of infinity of a geometric progression is $\frac{4}{3}$ and the first term is $\frac{3}{4}$. The common ratio is
If $\frac{{a + bx}}{{a - bx}} = \frac{{b + cx}}{{b - cx}} = \frac{{c + dx}}{{c - dx}},\left( {x \ne 0} \right)$ then $a$, $b$, $c$, $d$ are in