1
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In the previous example,

2
00:00:02,790 --> 00:00:08,045
we talked about two different sequences 
that occur inside an infinite series.

3
00:00:08,045 --> 00:00:10,570
There's the sequence of individual terms

4
00:00:10,570 --> 00:00:13,503
(those are the pieces that 
are being added together);

5
00:00:13,503 --> 00:00:16,986
and then there's also the 
sequence of partial sums,

6
00:00:16,986 --> 00:00:21,551
where S-n means 
the sum of the first n terms.

7
00:00:21,551 --> 00:00:25,854
So S-4 would be the sum of
the first four terms and so on.

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00:00:25,854 --> 00:00:31,849
The idea is, if we look at the sequence 
of partial sums or the running total,

9
00:00:31,849 --> 00:00:39,468
we can say, if the limit of that 
sequence (as n goes to infinity)

10
00:00:39,468 --> 00:00:50,445
is equal to some number, 
which we call S, then the series

11
00:00:50,445 --> 00:00:56,896
sum as n goes from 
one to infinity of ‘a’-n,

12
00:00:56,896 --> 00:01:01,184
we say the series converges.

13
00:01:01,184 --> 00:01:07,267
And we actually say that the value 
of that sum is this value right here.

14
00:01:09,537 --> 00:01:12,972
We say that the series converges to S.

15
00:01:12,972 --> 00:01:15,633
If the limit does not exist—

16
00:01:15,633 --> 00:01:24,511
So if limit as n goes to infinity 
of S-n does not exist,

17
00:01:24,511 --> 00:01:38,087
we say the series converges--
[corrects self] Sorry, diverges.