Question

Упростите выражение. Факториал

Answer 1

$\displaystyle\frac1{n!}+\frac1{(n+1)!}=\frac1{n!}+\frac1{n!\cdot(n+1)}=\frac{n+1+1}{(n+1)!}=\frac{n+2}{(n+1)!}$

$\displaystyle\frac1{n!}-\frac1{(n-1)!}=\frac1{(n-1)!\cdot n}-\frac1{(n-1)!}=\frac{1-n}{n!}$