Intro to series, Geometric series and Convergence
A sequence is defined as a function whose domain is the set of positive integers. Typically a sequenc is written in subscript notation instead of function notation as shown below.
a1, a2, a3, a4, …. , an
A series is the sum of the terms of a sequence. For example if a sequence is 1, 2, 3, 4, 5 then the series is 1+2+3+4+5. In Calculus, the series discussed are usually infinite series.
Most of the discussion of sequences and series in calculus involves the idea of convergence. If the limit of a series exists, then the series converges. If the limit does not exist, then the series is said to diverge.
A Geometric Series is a series in which the quotient of two terms is a common value, called the common ratio.