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 s[n] denote its nth partial sum:
If the sequence s[n] has a limit, that is, if there is some s such that for all > 0 there exists some N > 0 such that |s[n] - s| < , then the series is called convergent, and we say the series converges. We write
The number s is called the sum of the series. If the series does not converge, the series is called divergent, and we say the series diverges.
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