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JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Binomial theorem for any index

  • question_answer
    If \[|x|<1\]then the coefficient of \[{{x}^{n}}\] in the expansion of \[{{(1+x+{{x}^{2}}+....)}^{2}}\]will be [Pb. CET 1989]

    A) 1

    B) n

    C) \[n+1\]

    D) None of these

    Correct Answer: C

    Solution :

    Given expression \[{{(1+x+{{x}^{2}}+.....)}^{2}}\] \[={{[{{(1-x)}^{-1}}]}^{2}}={{(1-x)}^{-2}}\] \[=(1+2x+3{{x}^{2}}+4{{x}^{3}}+....+(n+1){{x}^{n}}+n{{x}^{n-1}}+....)\] Therefore coefficient of \[{{x}^{n}}\] is\[(n+1)\].


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