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SSC Sample Paper SSC CGL - Sample Paper-14

  • question_answer
    The sum of the first 20 terms of the series \[\frac{1}{5\times 6}+\frac{1}{6\times 7}+\frac{1}{7\times 8}+......\] is

    A) 0.16                 

    B) 1.6

    C) 16                                

    D) 0.016

    Correct Answer: A

    Solution :

    First term \[=\frac{1}{5\times 6}=\frac{1}{5}-\frac{1}{6}\] Second term \[=\frac{1}{6\times 7}=\frac{1}{6}-\frac{1}{7}\] 20th term \[=\frac{1}{24\times 25}=\frac{1}{24}-\frac{1}{25}\] \[\therefore \] Required sum \[=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{24}-\frac{1}{25}\]             \[=\frac{1}{5}-\frac{1}{25}=\frac{5-1}{25}=\frac{4}{25}\]             = 0.16 


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