Let

be a sequence. We call the sum

an infinite series (or just a series) and denote it as

.

We define a second sequence, *s*[*n*], called the partial
sums,
by

,

,

,

or, in general,

.

We then define convergence as follows:

Given a series
let . If the sequence
or . The number |

Copyright © 1996 Department of Mathematics, Oregon State University

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