Hint: Consider using Stirling's approximation for .
Edit: Stirling's formula could be overkill for this. You may want to consider applying the ratio test for sequences instead.
So let . Now compute . If , then its convergent.
Can you proceed?
The question:
Describe the limiting behaviour of the following sequence. If the sequence converges, then state its limit.
I'm not sure how to evaluate this. I tried get some intuition of what's going on, but I'm struggling. Any advice?
Hint: Consider using Stirling's approximation for .
Edit: Stirling's formula could be overkill for this. You may want to consider applying the ratio test for sequences instead.
So let . Now compute . If , then its convergent.
Can you proceed?
An alternative:
and
so, the limit of the given sequence is
Fernando Revilla
I think Chris L T521 meant to try the ratio test to see if the limit is . In that case we would deduce that the limit of the sequence is :
Fernando Revilla