Then note the well known fact that (x^n)/(n!) -> 0 as n -> ∞; put this together with the above theorem and get:

x/((n!)^(1/n)) -> 0 as n -> ∞.

Since x is constant in the limit, we must have:

(n!)^(1/n) -> ∞ as n -> ∞, and it's positive infinity since n! > 1 for all n in N.

[replaced ? with ∞ for you - mathsisfun]

]]>Considering the sequence

`a(n)=(n!)^(1/n) ; n∈N`

Prove that

```
lim a(n) = +oo
n->+oo
```

..any suggestions?

]]>