WEBVTT

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In the previous example,

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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)

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is equal to some number, 
which we call S, then the series

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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.