The product (32),

Question:

The product (32), (32)1/6 (32)1/36 ... to ∞ is equal to

(a) 64

(b) 16

(c) 32

(d) 0

Solution:

(a) 64

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

$=32\left(1+\frac{1}{6}+\frac{1}{36}+\ldots \infty\right)$

$=32\left(\frac{1}{1-\frac{1}{6}}\right)[\because$ it is a G.P. $]$

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

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

$=2^{6}$

$=64$

 

 

 

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