Question Number 104939 by ~blr237~ last updated on 24/Jul/20
$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} }{\left({n}+\mathrm{1}\right)!\left(\mathrm{2}{n}+\mathrm{1}\right)}\:=\:\frac{\sqrt{\pi}}{\mathrm{2}}\: \\ $$