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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

    Σ6n(x-5)n(n+1)/(n+11)

    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)]
    n→inf

    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.
     
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