JEE Main & Advanced Mathematics Sequence & Series Question Bank Harmonic Progression

  • question_answer
    The harmonic mean of \[\frac{a}{1-ab}\] and \[\frac{a}{1+ab}\] is [MP PET 1996; Pb. CET 2001]

    A)   \[\frac{a}{\sqrt{1-{{a}^{2}}{{b}^{2}}}}\]

    B)   \[\frac{a}{1-{{a}^{2}}{{b}^{2}}}\]

    C) \[a\]

    D) \[\frac{1}{1-{{a}^{2}}{{b}^{2}}}\]

    Correct Answer: C

    Solution :

    \[H.M.=\frac{2\left( \frac{{{a}^{2}}}{1-{{a}^{2}}{{b}^{2}}} \right)}{\frac{a}{1-ab}+\frac{a}{1+ab}}=\frac{2{{a}^{2}}}{2a}=a\].


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