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JEE Main & Advanced Mathematics Sequence & Series Question Bank Relation between AP., GP. and HP.

  • question_answer
    If \[a\] and \[b\] are two different positive real numbers, then which of the following relations is true [MP PET 1982; MP PET 2002]

    A) \[2\sqrt{ab}>(a+b)\]

    B) \[2\sqrt{ab}<(a+b)\]

    C) \[2\sqrt{ab}=(a+b)\]

    D) None of these

    Correct Answer: B

    Solution :

    We know that \[A>G>H\] Where \[A\] is arithmetic mean, \[G\] is geometric mean and \[H\] is harmonic mean, then \[{{S}_{n}}=\frac{1}{4}n\,(n+1)\,(n+2)(n+3)\] \[\Rightarrow \] or \[(a+b)>2\sqrt{ab}\].


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