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AP EAMCET2007MathematicsSequences and Series

The sum of the series 3 4 8 - 3 5 4 8 12 + 3 5 7 4 8 12 16 -

Options

  1. A3 2 - 3 4
  2. B2 3 - 3 4
  3. C3 2 - 1 4
  4. D2 3 - 1 4

Correct answer

B. 2 3 - 3 4

Step-by-step solution

Given series is aligned & 3 4 8 - 3 5 4 8 12 + 3 5 7 4 8 12 16 - + 3 4 - 3 4 = & 3 4 + 3 4 8 - 3 5 4 8 12 + 3 5 7 4 8 12 16 - - 3 4 = & 1- 1 4 + 1 3 2 4 4 - 1 3 5 4 4 2 4 3 + - 3 4 = & [1+1 (- 1 4 )+ 1(1+2) 2 (- 1 4 )^2 . & . + 1(1+2)(1+4) 3 2 (- 1 4 )^3+ ]- 3 4 aligned aligned & = [1+ 1 1 ! (- 1 4 )+ 1(1+2) 2 ! (- 1 4 )^2+ . & . 1(1+2)(1+4) 3 ! (- 1 4 )^3+ . ]- 3 4 & = (1- 1 4 )^ -1 / 2 - 3 4 & = 2 3 - 3 4 aligned

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