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JH
Numerade Educator

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Problem 30 Easy Difficulty

Determine whether the series converges or diverges.
$ \displaystyle \sum_{n = 1}^{\infty} \frac {n!}{n^n} $

Answer

converges

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Video Transcript

let's use the comparison test to show that the Siri's converges. So here we have in factorial over into the end. So this is one times two times three all the way up to end than end and all the way up to end and times. So this is one half two thirds one number end two over end and over end. And this is less than or equal to one over end times two over and sense three over end all the way up to an hour. And these are all less than or equal to one so we can replace the sum with two over and swear. And this convergence, this is you could use the pee test with P equals two. And that's David than one, which implies conversions now by the comparison test. Our Siri's also converges