Sequence And Series Question 552
Question: If $ |x|<1 $ , then the coefficient of $ x^{5} $ in the expansion of $ (1-x){\log_{e}}(1-x) $ is
Options:
A) 1/2
B) 1/4
C) 1/20
D) 1/10
Show Answer
Answer:
Correct Answer: C
Solution:
$ (1-x){\log_{e}}(1-x) $ $ =(1-x)[ -x-\frac{x^{2}}{2}-\frac{x^{3}}{3}-\frac{x^{4}}{4}-\frac{x^{5}}{5}-……\infty ] $ Hence coefficient of $ x^{5}=\frac{1}{4}-\frac{1}{5}=\frac{1}{20} $ .
BETA
