Sequence And Series Question 35
Question: In the expansion of $ {{(e^{x}-1)}^{2}} $ , the coefficient of $ x^{4} $ will be
Options:
A) 1/12
B) 7/12
C) 5/12
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ e^{2x}-2e^{x}+1=1+\frac{2x}{1\ !}+\frac{{{(2x)}^{2}}}{2\ !}+\frac{{{(2x)}^{3}}}{3\ !}+\frac{{{(2x)}^{4}}}{4\ !}+…… $ $ -2{ 1+\frac{x}{1\ !}+\frac{x^{2}}{2\ !}+\frac{x^{3}}{3\ !}+\frac{x^{4}}{4\ !}+….. }+1 $
$ \therefore $ The coefficient of $ x^{4} $ $ =\frac{2^{4}}{4\ !}-2.\frac{1}{4\ !}=\frac{2}{4\ !}(2^{3}-1)=\frac{7}{12} $ .
BETA
