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SSC Sample Paper SSC CGL - Sample Paper-19

  • question_answer
    The sum \[\frac{1}{\sqrt{2}+1}+\frac{1}{\sqrt{3}+\sqrt{2}}+\frac{1}{\sqrt{4}+\sqrt{3}}+...+\frac{1}{\sqrt{100}+\sqrt{99}}\] is

    A) 9                     

    B) 10

    C) 11                                

    D) None of these

    Correct Answer: A

    Solution :

    \[\frac{1}{\sqrt{2}+1}+\frac{1}{\sqrt{3}+\sqrt{2}}+...+\frac{1}{\sqrt{100}+\sqrt{99}}\] \[=\sqrt{2}-1+\sqrt{3}-\sqrt{2}+...+\sqrt{100}-\sqrt{99}\] \[=10-1=9\]      


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