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Stuck simplifying (Power Series)

  1. Jan 20, 2013 #1
    Edit: Nevermind, figured it out. Thank you for reading


    Original problem:
    Find the interval of convergence
    [itex]\sum[/itex]n=1 xn / n * √(n) * 3n

    Ratio Test, right? an+1/a

    I get to here and I can't figure out how to get rid of the ns:

    lim n→∞ abs(x/3)* [n*√(n) / (n+1)*√(n+1)]

    Solution,
    They break apart evenly:
    (n/(n+1)) * (n/(n+1)**(1/2)

    (also, sorry this looks terrible. I'm not sure how to use the graphics options very well yet)
     
    Last edited: Jan 20, 2013
  2. jcsd
  3. Jan 20, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    Start with just the n/(n+1) part. Divide numerator and denominator by n and tell me what the limit of that is as n->infinity.
     
  4. Jan 20, 2013 #3
    Simplifies down to:
    limn→∞ abs(x)/3 * (1/(1+1/n))**(3/2) = abs(x)/3

    Thank you very much for your reply!
     
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