Series

Used in: Expectation

The Geometric Series

\sum _ {i=0}^ {\infty }$$\alpha ^ {i} =1+$\alpha$ +${\alpha }^2$ +$\cdots$ =$\frac{1}{1-a}$ for$|a|<1$

Infinite Series

Needs to be well-defined
Fact: limit exists and independent of order of summation if \sum _ {i=1}^ {\infty }$$|a_ {i}|<$\infty$
The order of summation may matter