Question Number 123809 by Dwaipayan Shikari last updated on 28/Nov/20
$$\frac{{log}\mathrm{2}}{\mathrm{1}^{\mathrm{2}} }−\frac{{log}\mathrm{3}}{\mathrm{2}^{\mathrm{2}} }+\frac{{log}\mathrm{4}}{\mathrm{3}^{\mathrm{2}} }−\frac{{log}\mathrm{5}}{\mathrm{4}^{\mathrm{2}} }+... \\ $$