Tackling the first we get:

Prove that this sequence converges.

when n=1

n=2

n=3

n=4

When n is even the term being added onto the sequence is 0.

when n=1,5,.....,4n-3

when n=3,7,..........,4n-1

I have all this information but I don't know what to do with it!

I was thinking of substituting 4n-3 and 4n-1 instead of but this only results in a divergent sequence. =(