Question

Derive this series expansion: (I was wondering if there was a way to do it other than the long way)

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

Answer 1

i would start with
\[\ln(1+x)-\ln(1-x)\]

Answer 2

That makes sense.

Answer 3

the expansion for
\[ln(1+x)\] is well known as
\[x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+...\] then you can replace x by -x to get the expansion for
\[\ln(1-x)\] and then add term by term

Answer 4

yep.
thanks.

Answer 5

yw