Question

Упростите выражение 1)(k-1)!/k! 2)1/k!-k^2+k/(k+2)!

Answer 1

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