Question Number 212360 by MrGaster last updated on 11/Oct/24
$$ \\ $$$$\:\:\:\:\:{T}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\left(\mathrm{4}{n}+\mathrm{1}\right)^{\mathrm{2}} }−\frac{\mathrm{1}}{\left(\mathrm{4}{n}+\mathrm{3}\right)^{\mathrm{2}} }\right. \\ $$
Answered by Berbere last updated on 15/Oct/24
$$=\underset{{n}\geqslant\mathrm{0}} {\sum}\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }={C}\:{catalane}\:{constante} \\ $$