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JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

  • question_answer
    The middle term in the expansion of \[{{\left( x+\frac{1}{2x} \right)}^{2n}}\], is  [MP PET 1995]

    A) \[\frac{1.3.5....(2n-3)}{n!}\]

    B) \[\frac{1.3.5....(2n-1)}{n!}\]

    C) \[\frac{1.3.5....(2n+1)}{n!}\]

    D) None of these

    Correct Answer: B

    Solution :

    Obviously the middle term \[={{\,}^{2n}}{{C}_{n}}{{(x)}^{n}}.{{\left( \frac{1}{2x} \right)}^{n}}\]\[=\frac{2n!}{n!.n!{{.2}^{n}}}=\frac{1.3.5....(2n-1)}{n!}\].


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