Function and Maclaurin series Function $f(x)=\frac{x^2+3\cdot\ e^x}{e^{2x}}$ need to be developed in Maclaurin series.
I can't find any rule to sum all fractions I've got...so any suggestion that helps?
Thanks

Hint:
$$ f(x)=\frac{x^2+3\cdot\ e^x}{e^{2x}} = f(x)={x^2e^{-2x}+3 \ e^{-x}} $$
$$ = x^2\sum_{k=0}^{\infty}\frac{(-2x)^k}{k!}+\dots .$$
Added:
$$  x^2\sum_{k=0}^{\infty}\frac{(-2x)^k}{k!}= \sum_{k=0}^{\infty} \frac{(-2)^k x^{k+2}}{k!}=\frac{1}{4}\sum_{k=2}^{\infty} \frac{(-2)^k x^{k}}{(k-2)!} .$$
Now, do the same with the other term.
