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STD 11 - 8. sequence and series — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 8. sequence and series4 Marks
MCQ
The product $(32)(32)^{1/6}(32)^{1/36} ...... to\,\, \infty $ is
  • A
    $16$
  • B
    $32$
  • ✓
    $64$
  • D
    $0$
✓

Answer

Correct option: C.
$64$
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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