11th Class Mathematics Other Series Question Bank Critical Thinking

  • question_answer The sum of n terms of the series \[\frac{1}{1+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{7}}+.........\] is   [UPSEAT 2002]

    A) \[\sqrt{2n+1}\]

    B) \[\frac{1}{2}\sqrt{2n+1}\]

    C) \[\sqrt{2n+1}-1\]

    D) \[\frac{1}{2}(\sqrt{2n+1}-1)\]

    Correct Answer: D

    Solution :

    Putting \[n=1\] \[s=\frac{1}{1+\sqrt{3}}=\frac{\sqrt{3}-1}{2}\] On checking, (d) is the correct option.

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