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JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Mock Test - Binomial Theorem

  • question_answer
    The coefficient of \[{{x}^{5}}\]in \[{{(1+2x+3{{x}^{2}}+...)}^{-3/2}}\]is \[\left( \left| x \right|<1 \right)\]

    A) 21                    

    B) 25

    C) 26                   

    D) none of these

    Correct Answer: D

    Solution :

    [d] \[{{(1+2x+3{{x}^{2}}+...)}^{-3/2}}={{[{{(1-x)}^{-2}}]}^{-3/2}}\] \[={{(1-x)}^{3}}=1-3x+3{{x}^{2}}-{{x}^{3}}\] Therefore, coefficient of \[{{x}^{5}}\]is 0.


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