find the limit of $\displaystyle a_n = \frac{e^n + e^{-n}}{e^{2n} - 1}$ an n approaches infinity
L'Hop's rule doesnt work and dividing the terms by e^2n doesnt work either. I do not know what process should be used.
You have only to consider that is ...
$\displaystyle a_{n} = \frac { e^{n} + e^{-n}}{ e^{2n}-1} = e^{-n}\cdot \frac{ e^{n} + e^{-n}}{ e^{n}-e^{-n}} $ (1)
... and then find the limit when n tends to infinity of the two term of (1)... not very difficult...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$