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Question
The value of 91/3 . 91/9 . 91/27 ... upto inf, is
Options
(a) 1
(b) 3
(c) 9
(d) none of these
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Solution
\[(b) 3\]
\[ 9^\frac{1}{3} \times 9^\frac{1}{9} \times 9^\frac{1}{27} \times . . . \infty \]
\[ = 9^\left( \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + . . . \infty \right) \]
\[\text{ Here, it is a G . P . with } a = \frac{1}{3}\text{ and } r = \frac{1}{3} . \]
\[ \therefore 9^\left( \frac{\frac{1}{3}}{1 - \frac{1}{3}} \right) \]
\[ = 9^\left( \frac{1}{2} \right) = 3\]
\[\]
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