Finding the Limit of a Convergent Sequence

[StrangeCharm]

Homework Statement

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.

Homework Equations

N/A

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.

 

[Stephen Tashi]

I tried finding the limit of the sequence as n-->infinity using L'Hopital's rule, but that got messy..

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