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1520 11.2 #2 Infinite Series Convergence Definition[br]https://youtu.be/ndiE_PnfgMQ[br]In the previous example,

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we talked about two different sequences [br]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 [br]are being added together.

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And then there's also the [br]sequence of partial sums,

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where S-n  means [br]the sum of the first n terms.

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S-4 would be the sum of[br] the first four terms and so on.

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The idea is, if we look at the sequence [br]of partial sums or the running total,

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we can say, if the limit of that [br]sequence (as n goes to infinity)

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

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sum as n goes from one to infinity of ‘a’-n, [br]we say the series converges.

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We actually say that the value [br]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 [br]of S-n does not exist,

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we say the series converges--[br][corrects self] Sorry, diverges.[br]