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BITSAT2023MathematicsSequences and SeriesActual

The sum to infinite term of the series 1+ 2 3 + 6 3^2 + 10 3^3 + 14 3^4 + is

Options

  1. A3
  2. B4
  3. C6
  4. D2

Correct answer

A. 3

Step-by-step solution

We have Multiplying both sides by 1 3 , we get Subtracting eqn. (ii) from eqn. (i), we get aligned & 2 3 S=1+ 1 3 + 4 3^2 + 4 3^3 + 4 3^4 + & 2 3 S= 4 3 + 4 3^2 + 4 3^3 + 4 3^4 + & 2 3 S= 4 3 1- 1 3 = 4 3 3 2 S=3 aligned

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