1. The problem statement, all variables and given/known data

Use the Ratio Test for series to determine whether each of the following series converge or diverge. Make Reasoning Clear.

(a)

(b)

2. Relevant equations

3. The attempt at a solution

(a) I let = sequence of partial sums then plugged everything into ratio test formula.

I ended up with:

I know that the limit equals 0 hence the series converges but not quite sure how to show that the limit cancels down to show 0 is "obvious"

Any help would be great, thanks.

(b) I let = sequence of partial sums then plugged everything into ratio test formula.

I ended up with:

I know that:

And that:

Hence the overall limit = infinity and so the series diverges; but, once again i'm not quite sure how to show that how the limits cancels down to show ∞ and 0 is "obvious"

Once again, any help would be great, thanks.