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Question
The product (32), (32)1/6 (32)1/36 ... to ∞ is equal to
Options
(a) 64
(b) 16
(c) 32
(d) 0
Solution
(a) 64
\[32 \times {32}^\frac{1}{6} \times {32}^\frac{1}{36} \times . . . \infty \]
\[ = {32}^\left( 1 + \frac{1}{6} + \frac{1}{36} + . . . \infty \right) \]
\[ = {32}^\left( \frac{1}{1 - \frac{1}{6}} \right) [\because \text{ it is a G . P } . ]\]
\[ = {32}^\left( \frac{6}{5} \right) \]
\[ = \left( 2^5 \right)^\left( \frac{6}{5} \right) \]
\[ = 2^6 \]
\[ = 64\]
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