Power Series Expansion for Logarithm of 1 + x/Corollary

Theorem

 * $\displaystyle \ln\left({1-x}\right) = -\sum_{n \mathop = 1}^\infty \frac {x^n} n$

Proof
By Power Series Expansion for Logarithm Function:


 * $\displaystyle \ln\left({1+x}\right) = \sum_{n \mathop = 1}^\infty \left({-1}\right)^{n-1} \frac {x^n} n$

Then: