Theorem: If  for a sequence we have , where q < 1, then .

Theorem: If  for a sequence we have , where q >1 1, then

We get

Using the definition of  n! = n * (n-1) * (n-2) * ... * 2 * 1, so n! = n * (n-1)!, we get

We divide numerator and denominator by the highest power of variable n appearing in the denominator, we divide by n we get

thus , and using the theorem, we get