# Series A finite series, or just a series, is a sum of all terms of a [[Sequence]]. If the sequence is infinite, then the series is known as an [[Infinite Series]]. ## Summation Rules $\sum_{a=1}^b c = bc$ ![[The Gauss Trick#^iaisqa]] ![[The Gauss Trick#^rygyu3]] ![[Sum of Squares of First N Integers#^z1v20k]] ![[Sum of Cubes of First N Integers#^x3uvpu]] (for further proofs and generalizations see https://brilliant.org/wiki/sum-of-n-n2-or-n3/) ## Well-Known Series ### Arithmetic Series ![[Arithmetic Series#^3b0qf5]] The above can be used to derive tricks for calculating the sum of first $n$ integers ([[The Gauss Trick]]), as well as [[The Trick for Quickly Calculating the Sum of First N Odd Integers|sum of first odd]], and [[The Trick for Quickly Calculating the Sum of First N Even Integers|sum of first even]] integers. ### Geometric Series ![[Geometric Series#^4zycdx]] ### Arithmetic-Geometric Series ![[Arithmetic-Geometric Series#^3peyiy]]