Question

Hi everyone! Does \sum_{n=1}^\infty(-1)^{n}\frac{n^n}{n!} Converge Absolutely, Conditionally, or diverge? I think it diverges but can someone check me? Thanks! :o)

Answer 1

\sum_{n=1}^\infty(-1)^{n}\frac{n^n}{n!}

Answer 2

shoot...one sec...

Answer 3

please click for the problem...sorry http://www.HostMath.com/Show.aspx?Code=%5Csum_%7Bn%3D1%7D%5E%5Cinfty(-1)%5E%7Bn%7D%5Cfrac%7Bn%5En%7D%7Bn!%7D

Answer 4

i get th original summation diveres, then when i do the absolute value test, it also diverges...but I need to be sure

Answer 5

basically the sequence i get when just plugging in 1 - 5 is -1, 2,-9/2, 32/3, -625/24
the when I do the absolute value of the summation i get the sequence 1, 2, 9/2, 32/3, 625/24
so I think that would tell me the entire summation diverges but I need to be sure? :o)

Answer 6

you're right it diverges

Answer 7

oh neat...thanks so much!