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JH
Numerade Educator

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Problem 26 Easy Difficulty

Use the Root Test to determine whether the series is convergent or divergent.
$ \displaystyle \sum_{n = 1}^{\infty} \frac {( - 2)^n}{n^n} $

Answer

Absolute Convergence by root test because $L=0<1$

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Video Transcript

let's use the root test to determine whether the Siri's conversions of averages Now first, let me go ahead and call this an and know that we can also write a n equals negative to over end to the end power using your laws of exponents. Now, the root tests requires you to look at the end through of a M. So I'll use our one of our formulas here. We know that we could always write this radical as X to the one over. And so here I'LL use this formula simplified for Anne. And then we're raising this to the one over and power and recall that if you're taking an expo nit like we have here eight of the bee and you raise that to another exponents, see, that's just the same as multiplying to be in the sea. So here we'll supply the end and the one over and cancel out your left over with the limit of negative to over end. This goes to zero, which is less than one. So the Siri's converges and that's by the root test. And that's our final answer