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SSC Sample Paper Mock Test-20 SSC CGL Tear-II Paper-1

  • question_answer
    The value of \[1-\frac{1}{20}+\frac{1}{{{20}^{2}}}-\frac{1}{{{20}^{3}}}+...\]correct to 5 places of decimal, is

    A) 1.05     

    B)  0.95238

    C)  0.95239

    D)  10.5

    Correct Answer: B

    Solution :

    Let \[S=1-\frac{1}{20}+\frac{1}{{{20}^{2}}}-\frac{1}{{{20}^{3}}}+...\] It is geometric series to infinity with first term, a = 1 and common ratio \[r=-\frac{1}{20}\] \[\therefore \]      \[{{S}_{\infty }}=\frac{a}{1-r}=\frac{1}{1-\left( -\frac{1}{20} \right)}=\frac{1}{1+\frac{1}{20}}=\frac{20}{21}\]\[=0.9523809\] \[\therefore \] The value correct of 5 places of decimal = 035238


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