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NDA 2011
Exam
NDA
Year
2011
Subject
Mathematics
Chapter
Sequences and Series

NDA 2011 · Mathematics · Sequences and Series

What is the sum of 3 + 1 3 + 1 3 3 + ?

What is the sum of \sqrt{3}+\frac{1}{\sqrt{3}}+\frac{1}{3 \sqrt{3}}+\ldots$ ?

Options

  1. A32\frac{\sqrt{3}}{2}
  2. B332\frac{3 \sqrt{3}}{2}
  3. C232\frac{2 \sqrt{3}}{2}
  4. D3\sqrt{3}

Correct answer

B. 332\frac{3 \sqrt{3}}{2}

Step-by-step solution

3+13+133+…\sqrt{3}+\frac{1}{\sqrt{3}}+\frac{1}{3 \sqrt{3}}+\ldots The given series is in G.P. an infinite series Here, first term =3=\sqrt{3} And common ratio =13∴=\frac{1}{3}\therefore Required sum =31−13=323=332=\frac{\sqrt{3}}{1-\frac{1}{3}}=\frac{\sqrt{3}}{\frac{2}{3}}=\frac{3 \sqrt{3}}{2}.
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