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Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,1520 11.2 #2 Infinite Series Convergence Definition\Nhttps://youtu.be/ndiE_PnfgMQ\NIn the previous example, 
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,we talked about two different sequences \Nthat occur inside an infinite series. 
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,There's the sequence of individual terms. 
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Those are the pieces that \Nare being added together. 
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And then there's also the \Nsequence of partial sums, 
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,where S-n  means \Nthe sum of the first n terms.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,, S-4 would be the sum of\N the first four terms and so on. 
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,The idea is, if we look at the sequence \Nof partial sums or the running total, 
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,we can say, if the limit of that \Nsequence (as n goes to infinity) 
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,is equal to some number, \Nwhich we call S, then the series
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,sum as n goes from one to infinity of ‘a’-n, \Nwe say the series converges. 
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,We actually say that the value \Nof that sum is this value right here. 
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,We say that the series converges to S. 
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,If the limit does not exist—
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So if limit as n goes to infinity \Nof S-n does not exist, 
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,we say the series converges--\N[corrects self] Sorry, diverges.\N