# Arithmetic-Geometric Infinite Series When $|r|<1$, the limit for sum of infinite terms of an [[Arithmetic-Geometric Sequence]] exists and can be calculated as: $\lim_{n \rightarrow \infty^+} S_n = -\frac{a}{r-1}+\frac{dr}{(r-1)^2}$ ^a597aa For a sum of finite terms see [[Arithmetic-Geometric Series]].