For part (i), if the question asks you to consider a certain expression, make sure you simplify it first and see how it is related to the main question before proceeding. Once done, the standard Method of Differences applies. Remember to use pencil to show the strike-outs.
Part (ii) should be manageable so long you understand the concept of converging series and its sum to infinity. It’s a standard concept being tested in the A Levels.
Part (iii) is a little tricky in a sense that you have to substitute suitable expressions in terms of n into the main question in order to show some sort of connections with the original series in (i), since the question asks you to. It’s a little bit of trial and error here. Once done you can evaluate the original series accordingly and you will get the answer that is required.
Hopefully this is clear enough. Should you have any other question feel free to ask me. Cheers and all the best! :)