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Alternating series convergence

  1. Mar 26, 2009 #1
    1. The problem statement, all variables and given/known data
    I have 2 McLaurin series.

    1) ln(1+x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 + .........

    2) ln (1-x) = -x - (x^2)/2 - (x^3)/3 - (x^4)/4 + .........

    3. The attempt at a solution

    I want to find the range of x values for which series 1) and 2) converge.

    For 1) I am using the alternating series test. I know how to test for convergence, but how do I find the range of x values for which it converges?

    Am I missing something very obvious?
     
  2. jcsd
  3. Mar 26, 2009 #2
    Try to write the expansions of ln(x+1) and ln(1-x) in sigma notation, and then i believe all you need to do is find the radius of convergence of that power series, and it will give you all the values of x for which the two series converge.
     
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