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JEE Main20205 Sep 2020Evening ShiftMathematicsSequences and SeriesActual

If the sum of the first 20 terms of the series log 7 1 / 2 x + log 7 1 / 3 x + log 7 1 / 4 x + … is 460 , then x is equal to:

Options

  1. A7 2
  2. B7 1 / 2
  3. Ce 2
  4. D7 46 / 21

Correct answer

A. 7 2

Step-by-step solution

Given log 7 1 / 2 x + log 7 1 / 3 x + log 7 1 / 4 x + … 20 times = 460 ⇒    ( 2 + 3 + 4 + … . . + 21 ) log 7 x = 460 ⇒    20 2 ( 2 + 21 ) log 7 x = 460 ⇒    log 7 x = 2 ⇒    x = 49

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