Let $R>2$ be a real number. Then, for any $n\geq 1$, it holds that
$$ \frac{ \exp(n R)+ 1}{\exp( n R) - \exp(\pi R/2)} \leq \exp( R/n^2).$$
How do I prove this?
Let $R>2$ be a real number. Then, for any $n\geq 1$, it holds that
$$ \frac{ \exp(n R)+ 1}{\exp( n R) - \exp(\pi R/2)} \leq \exp( R/n^2).$$
How do I prove this?