Sequence And Series Question 475
Question: In the expansion of $ (1+x+x^{2}){e^{-x}} $ , the coefficient of $ x^{2} $ is
Options:
A) 1
B) $ -1 $
C) 1/2
D) -1/2
Show Answer
Answer:
Correct Answer: C
Solution:
$ (1+x+x^{2}){e^{-x}}=(1+x+x^{2}) $ $ { 1-\frac{x}{1\ !}+\frac{x^{2}}{2\ !}-\frac{x^{3}}{3\ !}+……. } $ Coefficient of $ x^{2}=1.\frac{1}{2\ !}+1.( -\frac{1}{1\ !} )+1.1=\frac{1}{2\ !}=\frac{1}{2} $ .
BETA
