Question

The coefficient of $x^n$ in the expansion of $\frac{e^{7x}+e^x}{e^{3x}}$ is

• A. $\frac{4^{n-1}+{\left(-2\right)}^n}{n!}$
• B. $\frac{4^{n-1}+2^n}{n!}$
• C. $\frac{4^n+{\left(-2\right)}^n}{n!}$
• D. $\frac{4^{n-1}+{\left(-2\right)}^{n-1}}{n!}$

Answer 1

Answer: (C)

$\frac{e^{7x}+e^x}{e^{3x}}=e^{4x}+e^{-2x}$
$\therefore$ Coefficient of $x^n$ in $\left(e^{4x}+e^{-2x}\right)$
$=\frac{(4{)}^n}{n!}+\frac{(-2{)}^n}{n!}$