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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Sequences and Series

NDA 2013 · Mathematics · Sequences and Series

What is 0.9+0.09+0.009+ equal to?

What is 0.9+0.09+0.009+…0.9+0.09+0.009+\ldots equal to?

Options

  1. A1
  2. B1.01
  3. C1.001
  4. D1.1

Correct answer

A. 1

Step-by-step solution

S=910+9100+91000……∞S=\frac{9}{10}+\frac{9}{100}+\frac{9}{1000} \ldots \ldots \infty This is sum of infinite terms G.P. with common ratio r=110S=9101−110=910910=1\begin{aligned} & r=\frac{1}{10} \\ & \mathrm{ S}=\frac{\frac{9}{10}}{1-\frac{1}{10}}=\frac{\frac{9}{10}}{\frac{9}{10}}=1 \end{aligned}
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