Bonjour. Show that $$\sum{\frac{1}{n^{2+\cos{n}}}}$$ is a divergent serie. $$\\$$
My main problem is: If $\epsilon$ is “infinitely small positive real number” define $A_{\epsilon}$ as the set of all $n, |2+\cos n|\leq 1+\epsilon$ $(n \in A_{\epsilon}\iff-1\leq \cos n \leq -1+\epsilon)$. The divergence should come from the sum over $A_{\epsilon}$ but I have no idea to how to handle this. $$\\$$