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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Sequences and Series

NDA 2012 · Mathematics · Sequences and Series

What is the sum of the series 1-(1)/(2)+(1)/(4)-(1)/(8)+ equal to?

What is the sum of the series 1−12+14−18+…1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\ldots equal to?

Options

  1. A1/2
  2. B3/2
  3. C2
  4. D2/3

Correct answer

D. 2/3

Step-by-step solution

1,−12,14,−18S∞=a1−rr=−1/2a=1=13.\begin{aligned} & 1, \frac{-1}{2}, \frac{1}{4}, \frac{-1}{8} \\ & \mathrm{ S}_{\infty}=\frac{a}{1-r} \quad r=-1 / 2 \\ & a=1 \quad=\frac{1}{3}.\end{aligned}
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