# Sum of an Infinite Geometric Series

To examine the sum of all the terms of an infinite geometric sequence, we need to consider $S_n = \dfrac{u_1(1-r^n)}{1-r}$ when $n$ gets very large. If $\left|r\right|>1$, the series is said to be divergent and the sum infinitely large. For instance, when $r=2$ and $u_1=1$; $S_\infty=1+2+4+8+\cdots$ is infinitely large. If $\left|r\right|