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Power Series help please

  1. Apr 24, 2017 #1
    1. The problem statement, all variables and given/known data

    There are three problems that I am struggling with.

    1. ∑[k2(x-2)k]/[3k]
    2. ∑[(x-4)n]/[(n)(-9)n]
    3. ∑[2k(x-3)k]/[k(k+1)]

    3. The attempt at a solution

    On the first two I am having problems finding the end-points of the interval of convergence. I use the ratio test.

    1. ∑[k2(x-2)k]/[3k]
    Here I get I = (1,3)

    2. ∑[(x-4)n]/[(n)(-9)n]
    I = (-13,5)

    And in the last one I got the end-points but I am not sure why the left one would diverge.
    It says it diverges in the answers but I cannot see it.

    3. ∑[2k(x-3)k]/[k(k+1)]

    I = [5/2,7/2)

    I use the alternating series test to evaluate x=5/2 and it doesn't seem to go to zero. I do l'hopitals, but it always shows me that it diverges.
     
  2. jcsd
  3. Apr 24, 2017 #2

    FactChecker

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    You can tell immediately that this is wrong. The interval of convergence of this power series is centered at x=4. I could believe (3,5) but not (-13,5). (I don't know about the endpoints.)
    Look at this again. The terms are (-1)k/[k(k+1)] at x=5/2.
     
  4. Apr 25, 2017 #3

    vela

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    It would be really helpful if you showed your work. Simply writing down the wrong answer doesn't give us much to go on to figure out where your mistakes are.
     
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