$S = \frac{1}{1-r}$ and $T = 1 + r + r^2$

$S = 1-r$ and $T = \frac{1-r^3}{1-r}$

$S = \frac{1}{1+r}$ and $T = 1 - r + r^2$

$S = \frac{1}{r-1}$ and $T = 1 + r + r^2$