WEBVTT
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let's use the ratio test to determine whether the Siri's
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conversions or divergence to do that, We should look
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at this term Over here, this's our end.
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So let's end to the tenth Power Overnegative ten to
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the end, plus one power. And the ratio
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test involves this limit of the absolute value and plus
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one over. And and the answer to this limit
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will tell us whether the Siri's Khun may tell us
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whether the series conversions of laboratories now in the numerator
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Let's do that and read So we'LL have n plus
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one to the ten negative ten and Plus two still
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have the slum it over here as and goes to
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infinity for the denominator. Let's do that in Green
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and we just use our formula over here. Now
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let's go ahead and rewrite this before we take the
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limit we have and plus one to the ten and
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to the ten. And then here we could drop
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the absolute value. Just make sure you replace these
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minus signs, so we'LL have ten to the N
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plus one over ten to the and plus two.
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So for this fraction on the right, most fraction
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you could cancel all the tens up there and then
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you'LL have one left in the bottom. And also
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, if you take the limit of this expression over
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here, you can also write. This is and
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plus one over into the tent, and a limit
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of this is one to the ten, which is
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one. So we have one times one over his
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head. That's one over ten, which is less
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than one and therefore the Siri's converges by the ratio
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test, and that's our final answer.