WEBVTT
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don't let's determine whether the Siri's conversions or diverges first
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. Not that this is less than or equal to
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one over and square. Why? To see if
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this is true, Just multiply the denominators to the
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other side. And here, in order for this
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to be true, we should take and this ex
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for in here to be bigger than or equal to
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tool. So eventually if we take this sum here
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, if we're letting and be bigger than two,
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then this is smaller than this. And eventually Lee
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and his bigger than or equal to two because we
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started one and then we go all the way to
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infinity. So we passed two right away so I
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can go ahead and right this if you let's go
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and pull off that first term and then I have
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the sum from n equals two to infinity. The
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reason I'm doing this I'm pulling out the first term
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and rewriting the sum is because I would like to
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use comparison test. But if I want to compare
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our expression toe one over and square, I need
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end to be tour larger. And this is why
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I originally and started at one so I took that
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term out. Now I just have to to infinity
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so I can go ahead and replace this with one
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over and square and again this already using is this
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. This inequality is just using this fact here and
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then taking a sum on both sides. And then
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the plus one just came along for the ride here
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. Now I know that this Siri's here converges from
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section eleven point three. This is what we call
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P series, and P is bigger than one.
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In any time that happened. Opens. It's conversion
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. And if we just add one through a convergence
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Siri's, that's not going to change the fact that
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we still have a real number. So our Siri's
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is less than or equal to a conversion. Siri's
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Our Siri's is less than or equal to a conversion
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series. So by the comparison test, our Siri's
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also that Burgess Funny convergence, John, And that's
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our final answer