Original subtitles

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Today we're going to be talking about the theories test for convergence.

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And in this particular problem we're going to be using the PCCs test to determine whether or not the

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series won over and to the seventh and the series won over the third root of N to determine whether

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or not either of those series is convergent and the PCs test is one of the easiest convergence tests.

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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

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one over end to the P then this series will converge whenever P is greater than 1 the series will diverged

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whenever P is less than or equal to 1.

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So we have some series and we can get into this form here where we have 1 divided by race to the P and

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to some exponent here.

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Then we can use the value of p to determine whether or not the series is convergent.

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Obviously that's going to be really easy to do when we already have the series in this form.

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Sometimes we can simplify our series using algebra and end up with this form and then we can use PCD

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sets to determine convergence and the series test can also be helpful when we're dealing with comparison's

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series or limit comparison test because oftentimes we can use a series in the form one over end to the

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p as a comparison series for another series where we're not sure about the convergence.

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So again this can be really useful when we have a series in this form and we want to determine convergence

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again again all we look at is the value here of the exponent.

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So in this first series we have won over and to the seven.

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Well all we need to say is that exponent 7 7 is greater than the one we're only interested in whether

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it's greater then less than or equal to one it's greater than 1 and because 7 is greater than 1.

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Therefore we can say that this series here we'll call this one a Subhan that it converges because seven

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the exponent is greater than 1.

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So it's just as easy as that.

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This series here won over the third root of N may look a little bit different but what we remember is

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that when we have a route like this instead of writing the third route like this we can also write it

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like this where we have won over and raised to the one third power and number that a square root is.

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And to the one half.

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Third root is.

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And the one third like this so we can convert it to that form and then we can say here that our exponent

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is one third while one third is less than 1.

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So therefore because one third is less than one we can say that we'll call this series B 7 we can say

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that B Subban diverges because one third is less than 1 in the series test tells us that when we have

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a value for p less than or equal to 1 the series diverges so it's a simple as that.

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Like I said it's one of the easiest convergence tests when you have a series in this form exactly.

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Really easy to use but remember that you can also use pre-series as a helpful comparison test.