my question is:
Expand g(x) = (1 - 2x)^(-1) as a powers series in (x+2).
I don't even know where to start, can anyone help me
thanks in advance
What Tonio did was treat the fraction $\displaystyle \frac{1}{1- \frac{2}{5}(x+ 2)}$ as "$\displaystyle \frac{1}{1- r}$", the sum of a geometric series with $\displaystyle r= \frac{2}{5}(x+ 2)$. That is the simplest and best way to do this problem.
You could also taken derivatives of $\displaystyle f(x)= (1- 2x)^{-1}$ and use the formula for a Taylor's series at x= 2 or used the "generalized binomial theorem" to expand $\displaystyle (a+ b)^{-1}$ with a= 1, b= -2x.