The sum of an infinite geometric series is $3$. A series, which is formed by squares of its terms, have the sum also $3$. First series will be
$\frac{3}{2},\frac{3}{4},\frac{3}{8},\frac{3}{{16}},.....$
$\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{{16}},.....$
$\frac{1}{3},\frac{1}{9},\frac{1}{{27}},\frac{1}{{81}},.....$
$1, - \frac{1}{3},\,\frac{1}{{{3^2}}}, - \frac{1}{{{3^3}}},.....$
What will $Rs.$ $500$ amounts to in $10$ years after its deposit in a bank which pays annual interest rate of $10 \%$ compounded annually?
The sum of the first five terms of the series $3 + 4\frac{1}{2} + 6\frac{3}{4} + ......$ will be
The sum of few terms of any ratio series is $728$, if common ratio is $3$ and last term is $486$, then first term of series will be
Fifth term of a $G.P.$ is $2$, then the product of its $9$ terms is
If $x > 1,\;y > 1,z > 1$ are in $G.P.$, then $\frac{1}{{1 + {\rm{In}}\,x}},\;\frac{1}{{1 + {\rm{In}}\,y}},$ $\;\frac{1}{{1 + {\rm{In}}\,z}}$ are in