Q155 / 270 · NDA 2012 (Phase 2) · Mathematics

What is the sum of first eight terms of the series $1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\ldots \ldots ?$

  • A
    $\frac{89}{128}$
  • B
    $\frac{57}{384}$
  • Correct answer
    C
    $\frac{85}{128}$
  • D
    None of the above

Solution

$1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\ldots \ldots \ldots$ Sum of first ' $n$ ' terms of G.P. $S_n=1 \cdot \frac{\left(1-\left(-\frac{1}{2}\right)^8\right)}{1-\left(-\frac{1}{2}\right)}=\frac{1-\frac{1}{256}}{1+\frac{1}{2}}$ $=\frac{\frac{255}{256}}{\frac{3}{2}}=\frac{85}{128}$.

Hence, the correct answer is option: 'C'.

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