Series

Apr 3, 2023

Used in: Expectation

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

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