If $y = x + {x^2} + {x^3} + .......\,\infty ,\,{\rm{then}}\,\,x = $
$\frac{y}{{1 + y}}$
$\frac{{1 - y}}{y}$
$\frac{y}{{1 - y}}$
None of these
The sum of the first three terms of a $G.P.$ is $S$ and their product is $27 .$ Then all such $S$ lie in
If every term of a $G.P.$ with positive terms is the sum of its two previous terms, then the common ratio of the series is
In an increasing geometric progression ol positive terms, the sum of the second and sixth terms is $\frac{70}{3}$ and the product of the third and fifth terms is $49$. Then the sum of the $4^{\text {th }}, 6^{\text {th }}$ and $8^{\text {th }}$ terms is :-
If ${a^2} + a{b^2} + 16{c^2} = 2(3ab + 6bc + 4ac)$, where $a,b,c$ are non-zero numbers. Then $a,b,c$ are in
If $a,\;b,\;c$ are in $G.P.$, then