Question

lim ((n+1)!+(n+2)!)/((n-1)!+(n+2)!) Помогите пожалуйста!!!

Answer 1

$limlimits _{n to infty} frac{(n+1)!+(n+2)!}{(n-1)!+(n+2)!} =\\star; ; (n+2)!=(n+1)!, cdot , (n+2)\\(n+2)!=(n-1)!, cdot , ncdot (n+1)cdot (n+2); ; ; star \\= limlimkits _{n to infty} frac{(n+1)!, cdot (1+n+2)}{(n-1)!, cdot (, 1+ncdot (n+1)cdot (n+2), )} =\\star ; ; (n+1)!=(n-1)!, cdot ncdot (n+1); ; star \\=limlimits _{n to infty}frac{(n-1)!, cdot ncdot (n+1)cdot (n+3)}{(n-1)!, cdot (, 1+ncdot (n+1)cdot (n+2), )} =limlimits _{n to infty}frac{ncdot (n+1)cdot (n+3)}{1+ncdot (n+1)cdot (n+3)} =$

$= limlimits _{n to infty} frac{n^3+4n^2+3n}{n^3+3n^2+2n+1} = limlimits _{n to infty} frac{1+frac{4}{n}+frac{3}{n^2}}{1+frac{3}{n}+frac{2}{n^2}+frac{1}{n^3}} =1$