Values that make series converge

Find the values for for which the following series converge:

1.

Attempted solution:

I tried to use the root test to evaluate and found that it is equal to . I got stuck here so I tried to use the ratio test and got to . And I'm stuck here for this method as well.

2.

Attempted solution:

I thought the only useful test would be the ratio test. So I tried it and got

however then I found which implies all values make this series converge, but that doesn't seem right.

Any suggestions would be appreciated. Thanks in advance.