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The power series above is the Taylor series....

  1. Apr 3, 2016 #1
    1. The problem statement, all variables and given/known data
    http://imgur.com/1aOFPI7

    PART 2

    2. Relevant equations
    Taylor series form

    3. The attempt at a solution
    My thought process is that the answer is 3 because using the geometric series equation (1st term)/(1-R) then you can get the sum. In this case R would be x+2 where x is -2 so 0. 1st term is 3/1 so the answer would be 3. I feel like this isn't what I'm supposed to do as it's saying the power series is the taylor series of some function, f but I have no idea how I could find a sum for that.
     
  2. jcsd
  3. Apr 3, 2016 #2

    Charles Link

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    Homework Helper

    I will try to help, but the PF rules don't allow me to give the complete answer. You are already very close to the correct answer using S=A/(1-R). Your R=x+2 is also correct. One hint is that the (x-a) shows up repeatedly in the Taylor expansion about x=a. You need to determine what "a" is in their Taylor expansion. Then try expanding your S(x) about x=a. Does this duplicate their function?
     
  4. Apr 3, 2016 #3
    So it's 3? A is -2...
     
  5. Apr 3, 2016 #4

    Charles Link

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    Homework Helper

    I just edited my post so that "A" and "a" are not confused. Yes, the expansion is about a=-2. For x=-2 the answer is 3. (This question wasn't clear in the link-it wants the sum of the series for...and the next character or two I couldn't see.) They also want to know the interval of convergence. That should be evident from your geometric series expression.
     
    Last edited: Apr 3, 2016
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