Question

Помогите вычислить предел....

Answer 1

$limlimits _{n to infty} frac{(n+1)!-2n!}{2(n+1)!+3n!} = limlimits _{n to infty} frac{frac{(n+1)!}{n!}-frac{2n!}{n!}}{frac{2(n+1)!}{n!}+frac{3n!}{n!}} = limlimits _{n to infty} frac{(n+1)-2}{2(n+1)+3} =\\= limlimits _{n to infty} frac{n-1}{2n+5} = limlimits _{n to infty} frac{frac{n}{n}-frac{1}{n}}{frac{2n}{n}+frac{5}{n}} = limlimits _{n to infty} frac{1-frac{1}{n}}{2+frac{3}{n}} = frac{1-0}{2+0} = frac{1}{2}$