- #1
greenteacup
- 6
- 0
Homework Statement
[tex]\sum[/tex][tex]^{\infty}_{n=1}[/tex] [tex]\frac{e^{n}+n}{e^{2n}-n^{2}}[/tex]
Homework Equations
I have to use either the Comparison Test or the Limit Comparison Test to show whether the series converges or diverges.
The Attempt at a Solution
[tex]a_{n}[/tex] = [tex]\frac{e^{n}+n}{e^{2n}-n^{2}}[/tex]
[tex]b_{n}[/tex] = [tex]\frac{1}{e^{2n}}[/tex]
[tex]lim_{n->\infty}[/tex] [tex]\frac{e^{n}+n}{e^{2n}-n^{2}}[/tex] * [tex]e^{2n}[/tex]
Annnd I'm not sure what to do beyond this point. I'm not even sure I'm taking the right equation for b[tex]_{n}[/tex]... Is it okay to just ignore the [tex]e^{n}[/tex] in the numerator like that?