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Numerade Educator

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Problem 4 Easy Difficulty

Use the Integral Test to determine whether the series is convergent or divergent.
$ \displaystyle \sum_{n = 1}^{\infty} n^{-0.3} $

Answer

The given series diverges

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Video Transcript

we can see that this function is a positive, decreasing function so we can use the interval test to do so. We we're going to evaluate the in cruel from one to infinity of X to the negative point three power. And of course, to solve this, we need to use a limit. And while we may initially think that because we have a negative exponents that we will and it was a converted, integral will find out it is different, Uh, in this case because when the anti differentiate But we'll still have a positive exponents. Yes, we have tea to the point seven power minus one and that will ah t to the point seven will go off to infinity. So that limit itself. It's infinity. So we know that the Siri's is then going to be a diversion