Question

запишите в виде дроби
1/(k-1)! - k/(k+1)!

Answer 1

$frac{1}{(k-1)!} - frac{k}{(k+1)!} = frac{1}{1cdot 2cdot ...cdot (k-2)cdot (k-1)} - frac{k}{1cdot2cdot ...cdot (k-1)cdot kcdot (k+1)}=\\=frac{kcdot (k+1)-k}{1cdot2cdot ...cdot (k-1)cdot kcdot (k+1)}=frac{k^2}{(k+1)!}$