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April 20, 2014

Posted by **A.** on Tuesday, December 4, 2012 at 2:27pm.

---This is what I tried to do---

So I was thinking of taking the derivative of ln(1+x/1-x) and get 2/x^2-1

And then use the identity 1/1-x= sum x^k

So then it will be Sum (-2^k) (x^2k)

- MATH -
**Steve**, Tuesday, December 4, 2012 at 3:10pmyou have the right idea.

First, df/dx = -2/(1-x^2), but I'd do it like this:

f(x) = ln(1+x) - ln(1-x)

ln(1+x) = 0+x-x^2/2+x^3/3-x^4/4+x^5/5+...

ln(1-x) = 0-x-x^2/2-x^3/3-x^4/4-x^5/5-...

subtract to get

0 + 2x + 2x^3/3 + 2x^5/5 + ...

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