does the series n^n/(n!*exp^n) converges or diverges? and how?

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does the series n^n/(n!*exp^n) converges or diverges? and how?

Mathematics
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must converge, division by an increasing exponential will tend to 0
but this does not mean converges
no but it means it dose not diverge either, a second test is required

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so which test?
it seems from the test of limit un not = 0 as n tends to infinity, for this one i got it wrong, it is divergent, there is no particular value that will ultimately be arrived at,
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it diverges but i could not prove it
how i can prove that the limit is not zero
are you here?
yes but must go now, if you look up D'alemberts ratio test for positive terms on the web you will see, its handy enough
could you give me the link
http://commons.activemath.org/ActiveMath2/main/viewBook.cmd?book=LeAM_calculusUniversityRec&page=68
thanks

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