Question

The coefficient of $x^2$ in the expansion of $\frac{1+10x+x^2}{e^x}$is

• A. $-10$
• B. $-\frac{17}{2}$
• C. $-\frac{15}{2}$
• D. $-8$

Answer 1

Answer: (B)

$-\frac{17}{2}$

$(1+10x+x^2)e^{-x}$
$=(1+10x+x^2)\left({\sum }_{n=0}^{\infty }\frac{(-x{)}^n}{n!}\right)$
So coefficient of $x^2=-10+\frac{1}{2}+1$
$=\frac{-17}{2}$