The following function for discrete values of the variable has emerged from a piece of geometry.
$f(n)=\sum_{i=2}^{i=n}({cot\frac{pi}{4i}-cot\frac{pi}{4i+2}})+\frac{1}{2}cot\frac{pi}{4n+2}$ .
How does this behave? Is there an asymptote? If so, how can I find it?