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SSC Quantitative Aptitude Number System and its Operations Question Bank Number Series and Sequences (I)

  • question_answer
    The sum of the series \[1+0.6+0.06+0.006+0.0006+...\] is

    A) \[1\frac{1}{2}\]

    B) \[3\frac{2}{3}\]

    C) \[1\frac{2}{3}\]

    D) \[5\frac{3}{4}\]

    Correct Answer: C

    Solution :

    [c] \[1+0.6+0.06+0.006+0.0006+...\] \[=1+\frac{6}{10}+\frac{6}{100}+\frac{6}{1000}+...\] \[=1+6\left( \frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+... \right)\] \[=1+6\left( \frac{\frac{1}{10}}{1-\frac{1}{10}} \right)=1+6\left( \frac{1}{10}\times \frac{10}{9} \right)\] \[=1+\frac{6}{9}=1+\frac{2}{3}=1\frac{2}{3}\]


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