Question

The product 32, $\left(32{)}^{\frac{1}{6}}\right(32{)}^{\frac{1}{36}}$ ....... to $\infty$ is equal to

• A. 64
• B. 16
• C. 32
• D. none of these

Answer 1

The correct option is A

64

(a) 64

$32\times {32}^{\frac{1}{6}}\times {32}^{\frac{1}{36}}+....\infty$

$={32}^{(1+\frac{1}{6}+\frac{1}{36}+....\infty )}$ [$\because$ It is a G. P.]

$={32}^{\left(\frac{1}{1-\frac{1}{6}}\right)}$

$={32}^{\left(\frac{6}{5}\right)}$

$=(2^5{)}^{\left(\frac{6}{5}\right)}$

$=2^6$

$=64$