數學分析|有關n!的一個極限(多解)

Solution A:

We know that if

then

Let

then

So

Solution B:

Stirling's approximation:

So

Solution C:

To consider its natural logarithm first.

So

Solution D:

To consider its natural logarithm first.

And we need to use The O'Stolz theorem:

If

then

So

So