-
In the previous example,
-
we talked about two different sequences
that occur inside an infinite series.
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There's the sequence of individual terms
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(those are the pieces that
are being added together);
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and then there's also the
sequence of partial sums,
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where S-n means
the sum of the first n terms.
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So S-4 would be the sum of
the first four terms and so on.
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The idea is, if we look at the sequence
of partial sums or the running total,
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we can say, if the limit of that
sequence (as n goes to infinity)
-
is equal to some number,
which we call S, then the series
-
sum as n goes from
one to infinity of ‘a’-n,
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we say the series converges.
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And we actually say that the value
of that sum is this value right here.
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We say that the series converges to S.
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If the limit does not exist—
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So if limit as n goes to infinity
of S-n does not exist,
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we say the series converges--
[corrects self] Sorry, diverges.
