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Determine if the series converges or diverges (show your work): n! / nn

Determine if the series converges or diverges (show your work):

n! / nn

Math   Advanced-Math   
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Answer #1

Ans= In this series, we have to show that the sequence is decreasing, and since each term is positive the sequence converges. We can’t take the derivative, as x! doesn’t make sense for x real. But we note that if then , which is what we want to know.(where represents the team and represents the term of the series.

So we look at :

So,this series finally converges to zero.

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