The product $2^{\frac{1}{4}} \cdot 4^{\frac{1}{16}} \cdot 8^{\frac{1}{48}} \cdot 16^{\frac{1}{128}} \cdot \ldots .$ to $\infty$ is equal to
$2^{\frac{1}{2}}$
$2^{\frac{1}{4}}$
$2$
$1$
$0.14189189189….$ can be expressed as a rational number
If $a,\;b,\;c$ are in $A.P.$, then ${3^a},\;{3^b},\;{3^c}$ shall be in
Find the sum of the products of the corresponding terms of the sequences $2,4,8,16,32$ and $128,32,8,2, \frac{1}{2}$
Which term of the following sequences:
$\frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \ldots$ is $\frac{1}{19683} ?$
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 $P^{2}=(a b)^{n}$