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SSC Sample Paper SSC CGL - Sample Paper-10

  • question_answer
    The value of \[\frac{3}{{{1}^{1}}{{.2}^{2}}}+\frac{5}{{{2}^{2}}{{.3}^{2}}}+\frac{7}{{{3}^{2}}{{.4}^{2}}}+\frac{9}{{{4}^{2}}{{.5}^{2}}}+\frac{11}{{{5}^{2}}{{.6}^{2}}}+\]\[\frac{13}{{{6}^{2}}{{.7}^{2}}}+\frac{15}{{{7}^{2}}{{.8}^{2}}}+\frac{17}{{{8}^{2}}{{.9}^{2}}}+\frac{19}{{{9}^{2}}{{.10}^{2}}}\] is

    A)  \[\frac{1}{100}\]                                  

    B)  \[\frac{99}{100}\]

    C)  \[\frac{101}{100}\]                              

    D)  1

    Correct Answer: B

    Solution :

    Expression \[=\frac{3}{{{1}^{2}}{{.2}^{2}}}+\frac{5}{{{2}^{2}}{{.3}^{2}}}+\frac{7}{{{3}^{2}}{{.4}^{2}}}+....+\frac{17}{{{8}^{2}}{{.9}^{2}}}+\frac{19}{{{9}^{2}}{{.10}^{2}}}\] \[=\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{2}^{2}}} \right)+\left( \frac{1}{{{2}^{2}}}-\frac{1}{{{3}^{2}}} \right)+\left( \frac{1}{{{3}^{2}}}-\frac{1}{{{4}^{2}}} \right)\] \[...+\left( \frac{1}{{{8}^{2}}}-\frac{1}{{{9}^{2}}} \right)+\left( \frac{1}{{{9}^{2}}}-\frac{1}{{{10}^{2}}} \right)\] \[=\frac{1}{{{1}^{2}}}-\frac{1}{{{2}^{2}}}+\frac{1}{{{2}^{2}}}-\frac{1}{{{3}^{2}}}+\frac{1}{{{3}^{2}}}-\frac{1}{{{4}^{2}}}+......\] \[\frac{1}{{{8}^{2}}}-\frac{1}{{{9}^{2}}}+\frac{1}{{{9}^{2}}}-\frac{1}{{{10}^{2}}}\] \[=1-\frac{1}{{{10}^{2}}}\] \[=1-\frac{1}{100}=\frac{100-1}{100}=\frac{99}{100}\]


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