JEE Main2014MathematicsSequences and SeriesActual

The least positive integer n such that 1- 2 3 - 2 3^2 - .- 2 3^ n-1 < 1 100 , is:

Options

Correct answer

B. 5

Step-by-step solution

aligned &1- 2 3 - 2 3^2 2 3^ n-1 < 1 100 & 1- 2 3 [ 1 3 + 1 3^2 + 1 3^3 + 1 3^ n-1 ] < 1 100 & 1-2 [ 1 3 ( 1 3^n -1 ) ] 1 3 -1 < 1 100 & 1-2 [ 3^n-1 2.3^n ] < 1 100 & 1- [ 3^n-1 3^n ] < 1 100 & 1-1+ 1 3^n < 1 100 aligned 100 < 3^n Thus, least value of n is 5

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