# Finding the Limit of a Convergent Sequence

1. Apr 11, 2015

### StrangeCharm

1. The problem statement, all variables and given/known data
Determine whether the sequence converges or diverges. If it converges, find the limit.
Here's the sequence: http://www4a.wolframalpha.com/Calculate/MSP/MSP89541ea2ag9dg617bcd6000050d52e94i67ei593?MSPStoreType=image/gif&s=39&w=66.&h=44. [Broken]

2. Relevant equations
N/A

3. The attempt at a solution
I know that the sequence is convergent if the limit exists; however, I'm having difficulty finding the limit. I tried finding the limit of the sequence as n-->infinity using L'Hopital's rule, but that got messy. I'm not sure what to do, especially because of all the terms.

Last edited by a moderator: May 7, 2017
2. Apr 11, 2015

### Stephen Tashi

Find $lim_{n \rightarrow \infty} \frac{n}{n + \sqrt{n}}$ and then think about the effect of $(-1)^{n+1}$.