I am trying to prove that $\frac{50^n}{n!}$ converges to $0$. For that, I want to make use of $|a_n - L| < \varepsilon$. I then take
$$ \left|\frac{50^n}{n!} - 0\right| = \frac{50^n}{n!} < \varepsilon \notag $$
And using $\frac{1}{n!} < \frac{50^n}{n!} < \varepsilon$ I obtain $\varepsilon > \frac{1}{n!}$, so I could chose $N$ such that $N! > \frac{1}{\varepsilon}$. However, when I use my calculator to try that out, for say $N = 4$ or $\varepsilon > \frac{1}{24}$, it doesn't work. When plotting the sequence, I see that it doesn't begin to converge until $n \approx 130$. My calculator can't go up that high though, so I can't confirm. That's why I'm asking here, to check whether what I'm trying to do is even correct or not.
