$$\lim_{n \to \infty}\left(\left(3 \left(n + 2\right)! - \frac{n!}{\left(2 n\right)! + \left(n + 2\right)!}\right) + \left(n + 1\right)!\right) = \infty$$
$$\lim_{n \to 0^-}\left(\left(3 \left(n + 2\right)! - \frac{n!}{\left(2 n\right)! + \left(n + 2\right)!}\right) + \left(n + 1\right)!\right) = \frac{20}{3}$$
Más detalles con n→0 a la izquierda$$\lim_{n \to 0^+}\left(\left(3 \left(n + 2\right)! - \frac{n!}{\left(2 n\right)! + \left(n + 2\right)!}\right) + \left(n + 1\right)!\right) = \frac{20}{3}$$
Más detalles con n→0 a la derecha$$\lim_{n \to 1^-}\left(\left(3 \left(n + 2\right)! - \frac{n!}{\left(2 n\right)! + \left(n + 2\right)!}\right) + \left(n + 1\right)!\right) = \frac{159}{8}$$
Más detalles con n→1 a la izquierda$$\lim_{n \to 1^+}\left(\left(3 \left(n + 2\right)! - \frac{n!}{\left(2 n\right)! + \left(n + 2\right)!}\right) + \left(n + 1\right)!\right) = \frac{159}{8}$$
Más detalles con n→1 a la derecha$$\lim_{n \to -\infty}\left(\left(3 \left(n + 2\right)! - \frac{n!}{\left(2 n\right)! + \left(n + 2\right)!}\right) + \left(n + 1\right)!\right) = - \frac{1}{2} + 4 \left(-\infty\right)!$$
Más detalles con n→-oo