Ineed desperate or else ill fail.
which geometric series converges?

The series will converge if r^2<1, where r is the common ratio of the geometric sequence.

The first has an r=2, so it diverges

The second has an r=-4 so it diverges.

The third has an r=3 so it diverges.

The fourth has an r=1/2 so it converges.

So only the last one converges...