$0.14189189189...$ can be expressed as a rational number.

The sum of an infinite geometric progression is $\frac{4}{3}$ and the first term is $\frac{3}{4}$. The common ratio is

The sum of some terms of a $G.P.$ is $315$,whose first term and the common ratio are $5$ and $2$ respectively. Find the last term and the number of terms.

If $n$ geometric means between $a$ and $b$ are $G_1, G_2, ..., G_n$ and a single geometric mean is $G$,then the true relation is

Let the positive numbers $a_1, a_2, a_3, a_4$ and $a_5$ be in a $G$.$P$. Let their mean and variance be $\frac{31}{10}$ and $\frac{m}{n}$ respectively,where $m$ and $n$ are co-prime. If the mean of their reciprocals is $\frac{31}{40}$ and $a_3+a_4+a_5=14$,then $m+n$ is equal to $.........$.

The coefficient of $x^{49}$ in the expansion of $(x - 1)(x - \frac{1}{2})(x - \frac{1}{2^2}) \dots (x - \frac{1}{2^{49}})$ is equal to