Question

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

• A. $16$
• B. $32$
• C. $64$
• D. $0$

Answer 1

Answer: (A)

$16$

$\left(32\right)\left(32{)}^{1/6}\right(32{)}^{1/36}......$ to $\infty =(32{)}^{1+\frac{1}{6}.....\infty }$

sum of infinite GP = a=1 , r=$\frac{1}{6}$

$\frac{a}{1-r}=\frac{1}{1-6}=\frac{6}{5}$

$(32{)}^{\frac{6}{5}}=16$