WEBVTT
1
00:00:00.840 --> 00:00:03.399 A:middle L:90%
okay for this problem. Our radius of convergence are
2
00:00:03.399 --> 00:00:08.830 A:middle L:90%
is lim a as n goes to infinity into the
3
00:00:08.830 --> 00:00:14.349 A:middle L:90%
end over in plus one to the end plus one
4
00:00:17.039 --> 00:00:20.480 A:middle L:90%
. Okay, so we can rewrite that as limited
5
00:00:20.489 --> 00:00:24.949 A:middle L:90%
n goes to infinity of in over in plus one
6
00:00:25.739 --> 00:00:29.030 A:middle L:90%
to the power of end and then times one over
7
00:00:29.379 --> 00:00:35.049 A:middle L:90%
in plus one. Okay, so in divided by
8
00:00:35.049 --> 00:00:39.969 A:middle L:90%
n plus one to the power of n that's one
9
00:00:39.969 --> 00:00:44.380 A:middle L:90%
over e and then we're left with limit as in
10
00:00:44.380 --> 00:00:50.320 A:middle L:90%
approaches infinity of one over in plus one and this
11
00:00:50.420 --> 00:00:53.030 A:middle L:90%
is zero. So we have won over E which
12
00:00:53.030 --> 00:00:58.280 A:middle L:90%
is just some finite number time zero So we end
13
00:00:58.280 --> 00:01:00.869 A:middle L:90%
up with zero. So the radius of convergence here
14
00:01:00.880 --> 00:01:06.269 A:middle L:90%
is zero. The interval of convergence. We just
15
00:01:06.269 --> 00:01:07.040 A:middle L:90%
checked the end points on this case. We're just
16
00:01:07.040 --> 00:01:11.950 A:middle L:90%
checking zero here and we're checking to see whether or
17
00:01:11.950 --> 00:01:19.620 A:middle L:90%
not this is going to converge. There's just adding
18
00:01:19.620 --> 00:01:22.030 A:middle L:90%
up zero a bunch of times. So this this
19
00:01:22.030 --> 00:01:25.760 A:middle L:90%
is going to be zero to that is going to
20
00:01:25.760 --> 00:01:30.439 A:middle L:90%
work. Case will include zero, but nothing else
21
00:01:30.439 --> 00:01:33.549 A:middle L:90%
will be included in our interval of convergence Are interval
22
00:01:33.549 --> 00:01:38.450 A:middle L:90%
of convergence is just zero all by itself