What is going on here? I understand it somewhat.

Find the interval of convergence and power series representation for the function.

$\displaystyle f(x) = \dfrac{2}{3 - x} = \dfrac{2}{3} (\dfrac{1 }{1 - (x/3) } $

$\displaystyle = (\dfrac{2}{3})$Summation sign goes here - n = 0 to infinity$\displaystyle (\dfrac{x}{3})^{n}$ ??? - What is the meaning of the n power over $\displaystyle \dfrac{x}{3}$?

$\displaystyle = (2)$Summation sign goes here - n = 0 to infinity$\displaystyle \dfrac{1}{3^{n+1}} x^{n}$ ??? - What is the meaning of n and n + 1 powers here?

Below here makes sense

$\displaystyle |\dfrac{x}{3}|< 1$

$\displaystyle |x|< 3$

$\displaystyle R = 3$ ??

$\displaystyle I = (-3,3)$ - Interval of convergence