testing for convergence/divergence

I've got a few problems here I'm wanting some guidance over.

1.

Am I right in thinking the Ratio test is the one to use here?

I get

Do I use the Ratio Test again? I end up with

2.

Absolute convergence test?

|cos n|<1, thus the above series can be reduced down to

>>edit: sorry, made a mistake in the original post in the series equation. Now rectified.<<

3.

I'm thinking the Root test here?

then, since , we're left with just

Any/all of these on the right track or have I totally lost the plot here?

Cheers!