$$ \newcommand{\RR}{\mathbb{R}} \newcommand{\QQ}{\mathbb{Q}} \newcommand{\CC}{\mathbb{C}} \newcommand{\NN}{\mathbb{N}} \newcommand{\ZZ}{\mathbb{Z}} \newcommand{\FF}{\mathbb{F}} \renewcommand{\epsilon}{\varepsilon} % ALTERNATE VERSIONS % \newcommand{\uppersum}[1]{{\textstyle\sum^+_{#1}}} % \newcommand{\lowersum}[1]{{\textstyle\sum^-_{#1}}} % \newcommand{\upperint}[1]{{\textstyle\smallint^+_{#1}}} % \newcommand{\lowerint}[1]{{\textstyle\smallint^-_{#1}}} % \newcommand{\rsum}[1]{{\textstyle\sum_{#1}}} \newcommand{\uppersum}[1]{U_{#1}} \newcommand{\lowersum}[1]{L_{#1}} \newcommand{\upperint}[1]{U_{#1}} \newcommand{\lowerint}[1]{L_{#1}} \newcommand{\rsum}[1]{{\textstyle\sum_{#1}}} % extra auxiliary and additional topic/proof \newcommand{\extopic}{\bigstar} \newcommand{\auxtopic}{\blacklozenge} \newcommand{\additional}{\oplus} \newcommand{\partitions}[1]{\mathcal{P}_{#1}} \newcommand{\sampleset}[1]{\mathcal{S}_{#1}} \newcommand{\erf}{\operatorname{erf}} $$

Series

• In 12  First Examples we define infinite series and inifnite products, and study some basic examples.
• In 13  Convergence Tests we develop theorems (known as convergence tests) to help us determine when a series converges, even if we cannot find its value.
• In 14  Limits of Sums we look at limits of infinite series, a special case of the iterated limits studied previously.
• In 15  \blacklozenge Advanced Techniques we take a brief look at some advanced techniques for working with infinite series, including summation by parts and double summation
• In 16  \bigstar Rearrangement we explore the vast differences between conditionally convergent series and absolutely convergent series.