Find the Maclaurin series for $\displaystyle [e^(x+1)^2 - 1]/(x+1)^2$ EDIT: the lopsided parenthesis stands for ^( . I don't know why my latex code won't work.

Here's how far I got...

$\displaystyle 1 + (x+1)^2 + [(x+1)^4]/(2!) + [(x+1)^6]/(3!)...$

SUBTRACTED BY...

$\displaystyle 1 - (x^2+2x) + (x^2+2x)^2 - (x^2+2x)^3...$

I'd like to know the summation notion (aka general term) of the series as well if that's possible.

In case you were wondering, I split the expression into two parts with a common denominator and used the maclaurin series of $\displaystyle e^x$ and $\displaystyle 1/(1-x)$ as starting points.