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Alternating series convergence

  • Thread starter t_n_p
  • Start date
595
0
1. Homework Statement
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?
 
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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