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 $a,\;b,\;c$ are in $G.P.$, then
The ${20^{th}}$ term of the series $2 \times 4 + 4 \times 6 + 6 \times 8 + .......$ will be
If $A = 1 + {r^z} + {r^{2z}} + {r^{3z}} + .......\infty $, then the value of $r$ will be
The numbers $(\sqrt 2 + 1),\;1,\;(\sqrt 2 - 1)$ will be in
How many terms of the $G.P.$ $3, \frac{3}{2}, \frac{3}{4}, \ldots$ are needed to give the sum $\frac{3069}{512} ?$