Mathematics - Definite Integration Question with Solution | TestHub

For positive integers $\mathrm{k}=1,2,3$, n , let ${\mathrm{S}}_{\mathrm{k}}$ denotes the area of $△{\mathrm{AOB}}_{\mathrm{k}}$ (where ' O ' is origin) such that that $\angle {\mathrm{AOB}}_{\mathrm{k}}=\frac{\mathrm{k}\pi }{2\mathrm{n}},\mathrm{OA}=1$ and ${\mathrm{OB}}_{\mathrm{k}}=\mathrm{k}$. The value of the ${\lim }_{\mathrm{n}\to \infty }\frac{1}{{\mathrm{n}}^2}{\sum }_{\mathrm{k}=1}^{\mathrm{n}}{\mathrm{S}}_{\mathrm{k}}$ is -