How do I solve $\lim_{n \to \infty} \frac{n!}{2^{n+1}}$ I am trying to solve the limit $\lim_{n \to \infty} \frac{n!}{2^{n + 1}}$.
Since both $n!$ and $2^{n + 1}$ approach $\infty$ as $n \to \infty$, my thinking was that I had to take the derivative of both the numerator and the denominator. However, from my research, the derivative of $n!$ is very complicated, involving some gamma function that we haven't covered in the course yet.
Is there an easier, more intuitive approach to solving this problem without using L'Hopital's Rule?

$n! >(1)(2)(3^{n-2})$. Can you finish?
