The product (32)(32)^ 1/6 (32)^ 1/36 ...... to , , is - Vidyadip

Question

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

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Answer

c
(c) $(32)(32)^{1/6}(32)^{1/36} ......\infty $

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

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

$ = {(32)^{\frac{1}{{5/6}}}} = {(32)^{6/5}}$

$ = {2^6} = 64$.

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