I need help with the Taylor series. Finding first few non zero terms of a function. Something like ln(1-2x)

Question

anonymous · Answer

do you know the one for $\ln(1+x)$?

anonymous · Answer

Yes something like 1-x+x^2-x^3

anonymous · Answer

replace $x$ by $-2x$

anonymous · Answer

So should I just use something like substitution?

anonymous · Answer

could you at least start me off in the right direction. I'm just having a hard time setting this up

anonymous · Answer

we can do it by hand if you like, but i think it is easier to substitute

anonymous · Answer

oh and btw your expansion of $\ln(1+x)$ is not quite right
it should be 
$$x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+...$$ or 
$$\sum_{n=1}^{\infty}\frac{(-1)^{n+1}x^n}{n}$$

anonymous · Answer

then replace $x$ by $-2x$ and get 
$$-2x-\frac{(2x)^2}{2}-\frac{(2x)^3}{3}-...$$