Sequence And Series Question 365
Question: In the expansion of $ (e^{x}-1),({e^{-x}}+1) $ , the coefficient of $ x^{3} $ is
Options:
A) 0
B) 1/3
C) 2/3
D) 1/6
Show Answer
Answer:
Correct Answer: B
Solution:
$ (e^{x}-1)({e^{-x}}+1)=(e^{x}-1)( \frac{1+e^{x}}{e^{x}} ) $ $ =\frac{e^{2x}-1}{e^{x}}=e^{x}-{e^{-x}}=2{ x+\frac{x^{3}}{3!}+…. } $ \ The coefficient of $ x^{3}=2.\frac{1}{3!}=\frac{1}{3} $ .
BETA
