Use any method you can to decide the convergence of
i)
ii)
iii)
iv)
Technically you are looking at the limit of $\displaystyle \frac{\sqrt{x}}{\ln(x)}$ but the two limits are equal (as long as you go from the continuous to the discrete anyway). (If you are not convinced suppose otherwise and you will rapidly find a contradiction)
RonL
This one $\displaystyle \lim_{n \to {\infty}}\bigg(1+\frac{1}{n}\bigg)^{n}$ is the famous definiton for $\displaystyle e\approx{2.71828183...}$..which means the sum diverges by the n-th term test...if you want to see how this was derived(the limit) look here http://www.mathhelpforum.com/math-he...-tutorial.html