Infinite Series

Sequences and Series

Sequence is a succession of numbers formed according to some fixed rule. Example is

$1,~ 8,~ 27,~ 64,~ 125,~ ...$

which is a sequence so that the nth term is given by n3.

Series is the indicated sum of a sequence of numbers. Thus,

$a_1 + a_2 + a_3 + ... + a_n + ...$

is the series corresponding to the sequence $a_1,~ a_2,~ a_3,~ ... ,~a_n,~ ...$

Finite and Infinite Series