(n=0)Σ(∞) (-1)^n * (n) is an alternating series that describes 1 - 2 + 3 - 4 + ...
The alternating series will converge to some number if the 'An' terms go to zero as n goes to infinity, in this case 'An' = n
lim n -> ∞ n = ∞
'An' goes to infinity...
...and at this point I can't remember if that means the series diverges for sure (which I think it does), or if it means a different test is required.