Question Number 151956 by mathdanisur last updated on 24/Aug/21
$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{2k}^{\mathrm{2}} }\:\mathrm{arctan}\:\frac{\mathrm{2k}^{\mathrm{2}} \:-\:\mathrm{1}}{\mathrm{2k}^{\mathrm{2}} }\:=\:? \\ $$