Evaluating the limit $\lim_{n \rightarrow +\infty} \frac{e^n+e^{-n}}{e^{n+1}+e^{-n-1}}$ How would you solve the following limit? It's $\frac \infty \infty$ and L'Hospital doesn't seem to help:
$$\lim_{n \rightarrow +\infty} \frac{e^n+e^{-n}}{e^{n+1}+e^{-n-1}}$$

HINT: Divide the numerator and the denominator by $\mathrm{e}^n$:
$$
  \frac{e^n+e^{-n}}{e^{n+1}+e^{-n-1}} = \frac{1+e^{-2n}}{e+e^{-2n-1}}
$$
