WEBVTT
1
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from party, eh? And all. Turning Siri's
2
00:00:04.040 --> 00:00:15.990 A:middle L:90%
is the theories you write this out is a song
3
00:00:17.140 --> 00:00:37.759 A:middle L:90%
whose terms alternate between positive and negative. So that's
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what all straining Siri's is for Part B. First
5
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, we should note that on alternating Siri's could always
6
00:00:45.609 --> 00:00:51.500 A:middle L:90%
be written in the form this form right here or
7
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usually. Sometimes people like to write in this form
8
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, depending on the Siri's. So here, what
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we need is for being to be digging his ear
10
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off. We need that the limit of being a
11
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zero, and we need that The pianist are decreasing
12
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for all in. So here are conditions. So
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let's call these A, B and C are those
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already being used like he's a different amuse numbers here
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. Here's one two in three. So this is
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the answer for party under what conditions will on alternating
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Siri's converge well and also ending Syria's will converge when
18
00:02:00.569 --> 00:02:10.560 A:middle L:90%
one through three are satisfied. So that's our answer
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00:02:10.560 --> 00:02:14.389 A:middle L:90%
for part two, and after part three, let's
20
00:02:14.389 --> 00:02:15.810 A:middle L:90%
go ahead and look at the remainder. So if
21
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these conditions are satisfied, so that's assuming that the
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alternating Siri's converges. So here we have our ulcer
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, any Siri's, but since it doesn't matter what
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the starting point is, and this entire sum is
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equal to some number US. Bye, Assumption.
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We're saying that it converges from party now the remainder
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, after adding in terms, is given by s
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minus the impartial some. And this is by a
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theorem in your textbook alternating Siri's estimation there, Um
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, this says that the remainder satisfies this, but
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we know that in the limit that limit beyond equal
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zero. So this implies that the limit of our
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end equal zero. So this tells us that in
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the limit that the remainder, after adding in terms
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, goes to zero, and that's our final answer
36
--> A:middle L:90%
.