Would you like to inspect the original subtitles? These are the user uploaded subtitles that are being translated: 1 00:00:00,690 --> 00:00:04,410 Today we're going to be talking about the theories test for convergence. 2 00:00:04,500 --> 00:00:09,300 And in this particular problem we're going to be using the PCCs test to determine whether or not the 3 00:00:09,300 --> 00:00:15,150 series won over and to the seventh and the series won over the third root of N to determine whether 4 00:00:15,150 --> 00:00:21,540 or not either of those series is convergent and the PCs test is one of the easiest convergence tests. 5 00:00:21,540 --> 00:00:28,230 It tells us that if we have some series and it's in the form one over and raised to the power of P So 6 00:00:28,230 --> 00:00:36,850 one over end to the P then this series will converge whenever P is greater than 1 the series will diverged 7 00:00:37,110 --> 00:00:40,290 whenever P is less than or equal to 1. 8 00:00:40,470 --> 00:00:47,790 So we have some series and we can get into this form here where we have 1 divided by race to the P and 9 00:00:47,790 --> 00:00:49,480 to some exponent here. 10 00:00:49,740 --> 00:00:53,760 Then we can use the value of p to determine whether or not the series is convergent. 11 00:00:53,760 --> 00:00:58,510 Obviously that's going to be really easy to do when we already have the series in this form. 12 00:00:58,530 --> 00:01:05,080 Sometimes we can simplify our series using algebra and end up with this form and then we can use PCD 13 00:01:05,100 --> 00:01:10,550 sets to determine convergence and the series test can also be helpful when we're dealing with comparison's 14 00:01:10,550 --> 00:01:17,550 series or limit comparison test because oftentimes we can use a series in the form one over end to the 15 00:01:17,550 --> 00:01:23,010 p as a comparison series for another series where we're not sure about the convergence. 16 00:01:23,040 --> 00:01:28,920 So again this can be really useful when we have a series in this form and we want to determine convergence 17 00:01:29,080 --> 00:01:32,910 again again all we look at is the value here of the exponent. 18 00:01:32,910 --> 00:01:37,120 So in this first series we have won over and to the seven. 19 00:01:37,320 --> 00:01:44,790 Well all we need to say is that exponent 7 7 is greater than the one we're only interested in whether 20 00:01:44,790 --> 00:01:50,370 it's greater then less than or equal to one it's greater than 1 and because 7 is greater than 1. 21 00:01:50,370 --> 00:01:57,610 Therefore we can say that this series here we'll call this one a Subhan that it converges because seven 22 00:01:57,690 --> 00:02:00,350 the exponent is greater than 1. 23 00:02:00,390 --> 00:02:02,210 So it's just as easy as that. 24 00:02:02,340 --> 00:02:08,010 This series here won over the third root of N may look a little bit different but what we remember is 25 00:02:08,010 --> 00:02:12,990 that when we have a route like this instead of writing the third route like this we can also write it 26 00:02:12,990 --> 00:02:19,450 like this where we have won over and raised to the one third power and number that a square root is. 27 00:02:19,470 --> 00:02:20,750 And to the one half. 28 00:02:20,820 --> 00:02:21,480 Third root is. 29 00:02:21,510 --> 00:02:27,480 And the one third like this so we can convert it to that form and then we can say here that our exponent 30 00:02:27,570 --> 00:02:33,600 is one third while one third is less than 1. 31 00:02:33,750 --> 00:02:39,720 So therefore because one third is less than one we can say that we'll call this series B 7 we can say 32 00:02:39,720 --> 00:02:46,170 that B Subban diverges because one third is less than 1 in the series test tells us that when we have 33 00:02:46,170 --> 00:02:51,890 a value for p less than or equal to 1 the series diverges so it's a simple as that. 34 00:02:51,890 --> 00:02:56,620 Like I said it's one of the easiest convergence tests when you have a series in this form exactly. 35 00:02:56,640 --> 00:03:02,070 Really easy to use but remember that you can also use pre-series as a helpful comparison test. 4354