Infinite Sequences and Series

infinite sequence. An infinite sequence is a function ${S: \pint \mapsto \reals,}$ written as ${(a_1,a_2,\ldots,a_n,\ldots).}$ We denote infinite sequences with the notation ${\seq{a_n}{n=1}{\infty},}$ and say that ${a_n}$ is the ${n}$th term.