// 2 x \
|| - + - |
|| 3 3 |2 x| |
|| -------- for |- + -| < 1|
|| 2 |3 3| |
|| /1 x\ |
|| |- - -| |
|| \3 3/ |
oo + |< |
|| oo |
|| ___ |
|| \ ` |
|| \ -n n |
|| / n*3 *(2 + x) otherwise |
|| /__, |
||n = 0 |
\\ /
$$\begin{cases} \frac{\frac{x}{3} + \frac{2}{3}}{\left(\frac{1}{3} - \frac{x}{3}\right)^{2}} & \text{for}\: \left|{\frac{x}{3} + \frac{2}{3}}\right| < 1 \\\sum_{n=0}^{\infty} 3^{- n} n \left(x + 2\right)^{n} & \text{otherwise} \end{cases} + \infty$$
oo + Piecewise(((2/3 + x/3)/(1/3 - x/3)^2, |2/3 + x/3| < 1), (Sum(n*3^(-n)*(2 + x)^n, (n, 0, oo)), True))