WEBVTT
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Let's show that the following series is absolutely conversion.
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So to do this instead of looking at the original
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Siri's, we should look at the absolute value of
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the terms and then take the son and let me
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go ahead and rewrite that denominators and to the three
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over, too. Now we know that sign of
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any number in absolute value. It's no larger than
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what so I'LL go here and I'll just replace the
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new murder with the one and I'LL leave the denominator
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as it is so you can see him. I'm
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kind of setting myself up for comparison test due to
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the inequality that's due to this inequality over here and
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now this I can go ahead and obtain another upper
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bound. So let me just go ahead and remove
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the one in the denominator, and that will make
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the fraction larger because the new operators were the same
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. However, the denominator on the right is smaller
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, so smaller denominator means larger fraction. And now
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I know this Siri's over here, the Siri's conversions
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by the Pee test. It's a P Siri's with
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P equals three over to which is bigger than one
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, and that's when it converges. And now therefore
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, because of inequality. This means that our original
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Siri's no, by the comparison test our cirie,
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not theory, regional one, but the one that
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we had when we use absolute value. So by
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the comparison test this Siri's converges, and by definition
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it means that the original Siri's is absolutely commercial,
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So that's our final answer.