Question

The coefficient of $x^2$ in the expansion of $\frac{1-2x+3x^2}{e^x}$ is

• A. $\frac{7}{2}$
• B. $\frac{9}{2}$
• C. $\frac{11}{2}$
• D. $\frac{13}{2}$

Answer 1

The correct option is C $\frac{11}{2}$

$=(1-2x+3x^2)e^{-x}$
$=(1-2x+3x^2)\left(\sum _{n=0}^{\infty }\frac{{(-x)}^n}{n!}\right)$
So coefficient $x^2=3+2+\frac{1}{2}$
$=\frac{11}{2}$