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Find out where this power series converges

  1. May 27, 2012 #1
    1. The problem statement, all variables and given/known data
    Find out where this power series converges.

    Ʃ(xn2n) / (3n + n3)


    2. Relevant equations



    3. The attempt at a solution

    I'm trying to use the ratio test to solve it. I end up with the following equation, which I am unable to reduce further:

    pn = 2x (3n + n3)/[(3)(3)n+n3(1+1/n)3]
     
  2. jcsd
  3. May 27, 2012 #2
    My guess is, since [itex]3^n[/itex] goes to infinity faster than [itex]n^3[/itex] (exponentials are faster than polynomials), is that your ratios go to [itex]\frac{2}{3}x[/itex]. Tnen you want [itex]|x|<\frac{3}{2}[/itex]. Not sure what happens at the boundaries. To check the limit I guessed at, maybe use l'Hopital's rule 3 times?
     
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