• # 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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