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BITSAT2012MathematicsSequences and SeriesActual

If x is positive then the sum to infinity of the series 1 1+3 x - 1-3 x (1+3 x)² + (1-3 x)² (1+3 x)³ - (1-3 x)³ (1+3 x)⁴ is

Options

  1. A1 / 2
  2. B1 6 x
  3. C1 6 x(1+3 x)
  4. D1 2(1+3 x)

Correct answer

A. 1 / 2

Step-by-step solution

The series is a G.P. with common ratio = ( 1-3 x 1+3 x ) and | r |= | 1-3 x 1+3 x | is less than 1 since x is positive S _ = a 1- r = 1 1+3 x 1- - ( 1-3 x 1+3 x ) = 1 2

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