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Verifying a taylor series

  1. Sep 5, 2012 #1
    1. The problem statement, all variables and given/known data
    For this problem I am to find the values of x in which the series converges. I know how to do that part of testing of convergence but constructing the summation part is what I am unsure about.

    I am given the follwing:
    1 + 2x + [itex]\frac{3^2x^2}{2!}[/itex] +[itex]\frac{4^3x^3}{3!}[/itex]+ ...

    2. Relevant equations
    I looked up online about the taylor series expansion for ex because I noticed it looked familiar and compared it with the series

    The taylor series for ex is:
    1 + x + [itex]\frac{x^2}{2!}[/itex] +[itex]\frac{x^3}{3!}[/itex]+ ...=Ʃ[itex]^{∞}_{n=0}[/itex][itex]\frac{x^n}{n!}[/itex]

    3. The attempt at a solution
    What I did was pretty much just put [itex]\frac{(n+1)^nx^n}{n!}[/itex] and checked the terms to see if it works. It seems to work but I am just a bit unsure. I haven't worked with this stuff in a while so I just want to be sure if I did that part right.
     
    Last edited: Sep 5, 2012
  2. jcsd
  3. Sep 6, 2012 #2
    That looks correct. You should be able to see if it converges using the ratio test, just be careful with the limit.
     
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