Question

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

Answer 1

must converge, division by an increasing exponential will tend to 0

Answer 2

but this does not mean converges

Answer 3

no but it means it dose not diverge either, a second test is required

Answer 4

so which test?

Answer 5

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,

Answer 6

it diverges but i could not prove it

Answer 7

how i can prove that the limit is not zero

Answer 8

are you here?

Answer 9

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

Answer 10

could you give me the link

Answer 11

http://commons.activemath.org/ActiveMath2/main/viewBook.cmd?book=LeAM_calculusUniversityRec&page=68

Answer 12

thanks