for part (i), simply use the test for divergence

for part (ii), still thinking of the nicest way to do this. don't want to try something like the integral test if it's not necessary

for part (iii). rewrite as (you can use partial fractions, but you don't have to). this should be a telescopic sum. write out some of the terms so you can see which will cancel out and which will stay. take the limit as when done to see the sum