1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Radius of Convergence

  1. Apr 11, 2016 #1
    1. The problem statement, all variables and given/known data
    Find all values of x such that the given series would converge


    2. Relevant equations

    3. The attempt at a solution
    By doing the ratio test I found that
    lim 6n(x-5)n(n+1)/(n+11) * (n+12)/[6n+1(x-5)n+1(n+2)]

    equals 1/(6(x-5)) * lim (n+12)(n+1)/(n+11)(n+2)
    This limit = 1 so to solve for the x I set
    -1<1/6(x-5) and 1/6(x-5)<1 and found the (31/6)<x<(29/6)
    but apparently this is incorrect. What am I doing wrong?
  2. jcsd
  3. Apr 11, 2016 #2
    Here it looks like you flipped the wrong fraction.
    Ratio test is more like [tex]\lim_{n\rightarrow \infty} {\frac{f(n+1)}{f(n)}}[/tex]
    Where [itex]f[/itex] is the function under the sigma. In my understanding, this would flip the fraction the other way from what you have.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Radius Convergence Date
Complex Analysis/Radius of Convergence question. Apr 3, 2017
Radius of Convergence Dec 10, 2016
Finding the Radius of Convergence through Ratio Test Apr 23, 2016
Radius of Convergence Apr 19, 2016