limit( Sigma( sqrt(1/k),k goes from 1 to n), n goes to infinity)
What are you trying to prove? I see no propositions in your post. Are you trying to show divergence? We have
This is a p-series, with , so you should know that it diverges. If you want to prove it without relying on the properties of p-series, one way is to use the Integral Test. Show that diverges (and note that is positive, decreasing, and continuous on ).