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SSC Sample Paper Mock Test-2 SSC CGL Tear-II Paper-1

  • question_answer
    What is the value of \[\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{15}+\sqrt{16}}\]

    A)  4                                

    B)  3

    C)  2                                

    D)  1

    Correct Answer: B

    Solution :

    \[\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{15}+\sqrt{16}}\] On rationalization \[=\frac{1-\sqrt{2}}{1-2}+\frac{\sqrt{2}-\sqrt{3}}{2-3}+...+\frac{\sqrt{15}-\sqrt{16}}{15-16}\] \[=-1\,\,[11-\sqrt{2}+\sqrt{2}-\sqrt{3}+...+\sqrt{15}-\sqrt{16}]\] \[=-1\,\,[1-4]=3\]


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