What does $ \prod_{i = 2}^{ n-1} \frac{1}{i}$ converge to?

Question

What does $ \prod_{i = 2}^{ n-1} \frac{1}{i}$ converge to?

It boils down to $\frac{1}{2} * \frac{1}{3} * \frac{1}{4} * ... * \frac{1}{n-1}$

But is there a direct formula that gives me the same answer?

Answer 1

By the squeeze theorem

$$0\le \prod_{i=2}^{n-1}\frac1i=\frac1{(n-1)!}\le \frac1{n-1}\xrightarrow{n\to\infty}0$$ we get easily the result.