Finding the Limit of a Convergent Sequence

  • #1
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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. [Broken]

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.
 
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Answers and Replies

  • #2
Stephen Tashi
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I tried finding the limit of the sequence as n-->infinity using L'Hopital's rule, but that got messy..

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