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Finding the Limit of a Convergent Sequence

  1. Apr 11, 2015 #1
    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. jcsd
  3. Apr 11, 2015 #2

    Stephen Tashi

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    Science Advisor

    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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