1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook