$$\lim_{n\rightarrow \infty}\frac{1}{n^2}\sum^{n-1}_{k=1}\cot^2\left(\frac{k\pi}{n}\right)$$ $n>1,n\in N$
Try: $\displaystyle \lim_{n\rightarrow \infty}\cot^2 \frac{k\pi}{n} = \frac{n^2}{k^2 \pi^2}$ (where $\lim_{x\rightarrow 0}\sin x=x, \lim_{x\rightarrow 0}\cos x = 1$)
so $$\lim_{n\rightarrow \infty}\frac{n^2}{\pi^2 n^2}\bigg(1+\frac{1}{2^2}+\frac{1}{3^2}+\cdots \cdots +\frac{1}{(n-1)^2}\bigg) = \frac{1}{\pi^2}\left(1+\frac{1}{2^2}+\frac{1}{3^2}+\cdots\right) = \frac{1}{6}$$
can someone please explain me whats wrong in my try and also explain me right answer
