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The Value of 91/3 . 91/9 . 91/27 ... Upto Inf, is - Mathematics

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प्रश्न

The value of 91/3 . 91/9 . 91/27 ... upto inf, is 

विकल्प

  • (a) 1 

  • (b) 3 

  • (c) 9 

  • (d) none of these

MCQ
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उत्तर

\[(b) 3\]
\[ 9^\frac{1}{3} \times 9^\frac{1}{9} \times 9^\frac{1}{27} \times . . . \infty \]
\[ = 9^\left( \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + . . . \infty \right) \]
\[\text{ Here, it is a G . P . with } a = \frac{1}{3}\text{ and } r = \frac{1}{3} . \]
\[ \therefore 9^\left( \frac{\frac{1}{3}}{1 - \frac{1}{3}} \right) \]
\[ = 9^\left( \frac{1}{2} \right) = 3\]
\[\]

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अध्याय 20: Geometric Progression - Exercise 20.8 [पृष्ठ ५७]

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आरडी शर्मा Mathematics [English] Class 11
अध्याय 20 Geometric Progression
Exercise 20.8 | Q 9 | पृष्ठ ५७

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