sum e^n/(1+e^2n)
n = 1 to infinity
By using the integral test I need to integrate this to determine whether it will converge or diverge.
Can someone please help with the integration. I cannot figure out how to integrate it.
$\displaystyle du = e^n dn \implies dn = \frac{du}{e^n}$
$\displaystyle \therefore \int \frac{e^n}{1+e^{2n}} dn $
$\displaystyle = \int \frac{1}{1+u^2} du = tan^{-1}(u)$
plug back $\displaystyle u = e^n$, you have:
$\displaystyle [tan^{-1}(e^n)]_1^\infty$
now find out if the series converges or not!