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SSC Sample Paper SSC CGL - Sample Paper-29

  • 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) 0                                 

    B) 1

    C) 2                                 

    D) 3

    Correct Answer: D

    Solution :

    \[\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+....+\frac{1}{\sqrt{15}+\sqrt{16}}\] On rationalization \[=\frac{1-\sqrt{5}}{1-2}+\frac{\sqrt{2}-\sqrt{3}}{2-3}+...+\frac{\sqrt{15}-\sqrt{16}}{15-16}\] \[=-1[1-\sqrt{2}+\sqrt{2}-\sqrt{3}+...+\sqrt{15}-\sqrt{16}]\] \[=-[1-4]=3\]


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