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?

Printable View

- January 22nd 2011, 10:05 PMGlitchLimiting behavior of a sequence
**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? - January 22nd 2011, 10:08 PMChris L T521
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? - January 22nd 2011, 10:21 PMGlitch
Hmm, the ratio test seems to be much further into this chapter, which is beyond this problem set. I'll try it anyway, however It'd be interesting to know if there's another method.

- January 22nd 2011, 10:27 PMChris L T521
- January 22nd 2011, 10:44 PMGlitch
Ahh yep, that was fairly easy to work out after doing a bit of algebra. Thanks.

Odd that Stirling's approx. isn't mentioned in this text either. I think they wanted us to solve it via intuition. 0_o - January 22nd 2011, 11:18 PMFernandoRevilla
An alternative:

and

so, the limit of the given sequence is

Fernando Revilla - January 23rd 2011, 05:54 AMHallsofIvy
- January 23rd 2011, 09:12 AMFernandoRevilla
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 - January 23rd 2011, 09:42 AMChris L T521