The product $(32)(32)^{1/6}(32)^{1/36} ...... to\,\, \infty $ is
The product $(32)(32)^{1/6}(32)^{1/36} ...... to\,\, \infty $ is
- A
$16$
- B
$32$
- C
$64$
- D
$0$
Similar Questions
A $G.P.$ consists of an even number of terms. If the sum of all the terms is $5$ times the sum of terms occupying odd places, then find its common ratio.
A $G.P.$ consists of an even number of terms. If the sum of all the terms is $5$ times the sum of terms occupying odd places, then find its common ratio.
$2.\mathop {357}\limits^{ \bullet \,\, \bullet \,\, \bullet } = $
$2.\mathop {357}\limits^{ \bullet \,\, \bullet \,\, \bullet } = $
- [IIT 1983]
Let $P(x)=1+x+x^2+x^3+x^4+x^5$. What is the remainder when $P\left(x^{12}\right)$ is divided by $P(x)$ ?
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- [KVPY 2009]
If the sum of an infinite $GP$ $a, ar, ar^{2}, a r^{3}, \ldots$ is $15$ and the sum of the squares of its each term is $150 ,$ then the sum of $\mathrm{ar}^{2}, \mathrm{ar}^{4}, \mathrm{ar}^{6}, \ldots$ is :
If the sum of an infinite $GP$ $a, ar, ar^{2}, a r^{3}, \ldots$ is $15$ and the sum of the squares of its each term is $150 ,$ then the sum of $\mathrm{ar}^{2}, \mathrm{ar}^{4}, \mathrm{ar}^{6}, \ldots$ is :
- [JEE MAIN 2021]
The G.M. of the numbers $3,\,{3^2},\,{3^3},\,......,\,{3^n}$ is
The G.M. of the numbers $3,\,{3^2},\,{3^3},\,......,\,{3^n}$ is