Question Number 98848 by M±th+et+s last updated on 16/Jun/20
$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}+{k}+\mathrm{1}} \left(\mathrm{1}+{k}\right)^{\mathrm{2}} }{{n}\left({n}+{k}+\mathrm{1}\right)^{\mathrm{4}} } \\ $$