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Homework Help: Power series

  1. Oct 27, 2011 #1
    1. The problem statement, all variables and given/known data

    I've attached the question

    2. Relevant equations



    3. The attempt at a solution

    I'm not exactly sure how to do this question. Is it an interval of convergence question where i simply let log(1+2x) < 1 and solve for x??
     

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  2. jcsd
  3. Oct 27, 2011 #2

    Dick

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    It's actually more of a logic problem. They told you log(1+x) converges for |x|<1. So what's the range of convergence of log(1+2x)? You are overthinking this by quite a bit.
     
  4. Oct 27, 2011 #3

    Mark44

    Staff: Mentor

    No. What I would do is find the power series for log(1 + 2x), which is simply a matter of a substitution, and then determine the interval of convergence of the new series.

    BTW, calculus-type problems like this should not be posted in the Precalc section.
     
  5. Oct 27, 2011 #4

    Dick

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    I don't think it's even much of a precalc question. See my previous post.
     
  6. Oct 27, 2011 #5

    Mark44

    Staff: Mentor

    I agree that it's not a difficult problem, but being about series and convergence, it seems a better place for it is in the Calculus & Beyond section.
     
  7. Oct 28, 2011 #6

    Dick

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    Your choice, of course. But I don't think you need any convergence tests to answer the question. x is a number, 2x is a number.
     
  8. Oct 28, 2011 #7
    so your saying the answer is simply |2x| < 1?
     
  9. Oct 28, 2011 #8
    Okay I understand how to do interval of convergences but how would I get the new series through substitution?
     
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