JEE Main & Advanced Mathematics Other Series Question Bank Critical Thinking

  • question_answer If  \[|x|<1\], then the coefficient of \[{{x}^{5}}\] in the expansion of \[(1-x){{\log }_{e}}(1-x)\] is

    A) 1/2

    B) 1/4

    C) 1/20

    D) 1/10

    Correct Answer: C

    Solution :

    \[(1-x){{\log }_{e}}(1-x)\] \[=(1-x)\left[ -x-\frac{{{x}^{2}}}{2}-\frac{{{x}^{3}}}{3}-\frac{{{x}^{4}}}{4}-\frac{{{x}^{5}}}{5}-......\infty  \right]\]   Hence coefficient of \[{{x}^{5}}=\frac{1}{4}-\frac{1}{5}=\frac{1}{20}\].

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