If $1\, + \,\sin x\, + \,{\sin ^2}x\, + \,...\infty \, = \,4\, + \,2\sqrt 3 ,\,0\, < \,x\, < \,\pi $ then
$x = \frac{\pi }{6}$
$x = \frac{\pi }{3}$
$x = \frac{\pi }{6}$ or $\frac{\pi }{3}$
none of these
If $y = x + {x^2} + {x^3} + .......\,\infty ,\,{\rm{then}}\,\,x = $
If the $4^{\text {th }}, 10^{\text {th }}$ and $16^{\text {th }}$ terms of a $G.P.$ are $x, y$ and $z,$ respectively. Prove that $x,$ $y, z$ are in $G.P.$
The first two terms of a geometric progression add up to $12.$ the sum of the third and the fourth terms is $48.$ If the terms of the geometric progression are alternately positive and negative, then the first term is
The product $(32)(32)^{1/6}(32)^{1/36} ...... to\,\, \infty $ is