Convergence/Divergence of Series.

I am really poor in this part, been trying to do as much exercises as possible to get familiar with the patterns and I realised there are these few patterns that I couldn't seem to approach it.

Sometimes I know the right approach for it, but I have troubles simplifying the terms in order to prove that it fits certain criteria required to do conclusions. Here are a few cases, I hope that you guys would be able to give me a guidance on how to approach these different cases.

**Case I** : When there is root of something involved.

(i)

(ii)

(iii)

**Case II** : When there is to the power of n.

(i)

(ii)

I reckon you approach this one with the ratio test? I always have troubles simplifying them!

**Case III** : When there is polynomials.

(i)

(ii)

And the following few questions, I don't know how to classify them.

(i) - Alternating Series??

(ii)

(iii) - I suppose you use Ratio test? But I have troubles simplifying this one!

Quite a number of questions there, I know! So sorry for the overload of questions :( Thanks for looking and helping though!!

Your help to master this topic would be greatly greatly appreciated!

Thank you so much!