WEBVTT
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What can we conclude by applying the πth of term divergence test in the series the sum from π equals one to β of two π over six π squared add four.
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Letβs take a look at the πth term divergence test.
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This says that if the limit as π approaches β of ππ is not equal to zero, then the sum of ππ diverges.
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If the limit as π approaches β of aπ equals zero, then the sum of ππ may or may not converge.
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So, what this is telling us is that we need to find the limit as π approaches β of two π over six π squared add four.
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To do this, we remember that when we take a limit at β for a polynomial, all we need to do is look at the term with the largest power.
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The degree of the numerator is one.
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And the degree of the denominator is two.
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And so, because the numerator has a smaller degree than the denominator, this limit is equal to zero.
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So, weβre in this scenario, since we found the limit to be zero.
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So, this may or may not converge.
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Therefore, the divergence test is inconclusive.