Question

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

विकल्प

• (a) 64

• (b) 16 

• (c) 32 

• (d) 0 

Answer 1

(a) 64 

\[32 \times {32}^\frac{1}{6} \times {32}^\frac{1}{36} \times . . . \infty \]
\[ = {32}^\left( 1 + \frac{1}{6} + \frac{1}{36} + . . . \infty \right) \]
\[ = {32}^\left( \frac{1}{1 - \frac{1}{6}} \right) [\because \text{ it is a G . P } . ]\]
\[ = {32}^\left( \frac{6}{5} \right) \]
\[ = \left( 2^5 \right)^\left( \frac{6}{5} \right) \]
\[ = 2^6 \]
\[ = 64\]