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Power Series

  1. Nov 11, 2014 #1
    1. The problem statement, all variables and given/known data

    n=3 ∑ ((-1)n (x+3)3n)/(2nlnn)

    Find radius of convergence, interval of convergence, values for x which series is: absolutely convergent, conditionally converge or divergence.

    2. Relevant equations


    3. The attempt at a solution
    I applied the Ratio Test and got

    |(x+3)3| lim n--> ∞ (-1(lnn))/(ln(n+1))

    Then I used l'Hospitals to get the limit and got -1/2.
    So then it's -1/2 * |(x+3)3| = L. Then do the radius and interval stuff.

    The problem is that it's -1/2 and the radius can't be negative. I've had one or two similar problems where I keep getting a negative radius. Not sure what I am missing.
     
  2. jcsd
  3. Nov 11, 2014 #2
    The absolute value of -1 is 1. When you're pulling out the (x+3)^3, you have to keep the absolute value on the lnn/ln(n+1) or pull out the -1 with the (x+3)^3. Also I am pretty sure you're missing (1/2) somewhere in your limit.
     
  4. Nov 11, 2014 #3
    Wow, did not even know that. Solves the negative radius I was having with the other problems.
    Thanks alot!

    Yea, I forgot the 2 in the denominator of the limit.
     
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