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1520 11.2 #2 Infinite Series Convergence Definition
https://youtu.be/ndiE_PnfgMQ
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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 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, 
we say the series converges. 

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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.