The number which should be added to the numbers $2, 14, 62$ so that the resulting numbers may be in $G.P.$, is
$1$
$2$
$3$
$4$
Find the sum of the following series up to n terms:
$5+55+555+\ldots$
Insert two numbers between $3$ and $81$ so that the resulting sequence is $G.P.$
The sum of the series $3 + 33 + 333 + ... + n$ terms is
If the first and the $n^{\text {th }}$ term of a $G.P.$ are $a$ and $b$, respectively, and if $P$ is the product of $n$ terms, prove that $P^{2}=(a b)^{n}$
The greatest integer less than or equal to the sum of first $100$ terms of the sequence $\frac{1}{3}, \frac{5}{9}, \frac{19}{27}, \frac{65}{81}, \ldots \ldots$ is equal to