Does the Series (-1)^n((n+1)^(1/2)-n^(1/2) Converge or Diverge?; Using the Alternating Series Test

Being that this is an alternating series, we can apply the alternating series test to see if the series meets all of the requirements to be convergent. If not, then the Alternating Series Test is inconclusive and we must try another test. But in this case its pretty straightforward.