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AP EAMCET201825 Apr 2018Morning ShiftMathematicsSequences and SeriesActual

1 4 - 5 4 · 8 + 5 · 9 4 · 8 · 12 - … =

Options

  1. A3 3 - 2 5 9 3
  2. B2 3 - 3 2 9 3
  3. C2 1 4 - 1 2 1 4
  4. D2 3 - 3 5 9 3

Correct answer

C. 2 1 4 - 1 2 1 4

Step-by-step solution

We have, 1 4 - 5 4 · 8 + 1 · 5 · 9 4 · 8 · 12 - … … = 1 4 - 1 · 1 + 4 2 ! 1 4 2 + 1 · 1 + 4 1 + 2 · 4 3 ! 1 4 3 - … … = 1 1 4 - 1 · 1 + 4 2 ! 1 4 2 + 1 · 1 + 4 1 + 2 · 4 3 ! 1 4 3 - … …     . . . i Now, we know that 1 + x - p q = 1 - p x q + p p + q 2 ! x q 2 - … … … … Therefore, from i , we have = 1 1 4 - 1 · 1 + 4 2 ! 1 4 2 + 1 · 1 + 4 1 + 2 · 4 3 ! 1 4 3 - … … =

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