Definition:
Series, Partial Sums, and Convergence
Let
{a
n
}
be an infinite sequence.
The formal expression
is called an (infinite)
series
.
For
N = 1, 2, 3, ...
the expression
S
N
=
is called the
N-th partial sum
of the series.
If
lim S
N
exists and is finite, the series is said to
converge
.
If
lim S
N
does not exist or is infinite, the series is said to
diverge
.
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(bgw)
is called an (infinite) series.
is called the N-th partial sum of the series.
is called an (infinite) series.
is called the N-th partial sum of the series.
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