And in b) do you mean:
or something else? The first and the last definition is definitely divergent, because they are both bigger than , which is definitely divergent. The second definition converges, because it can be rewritten as:
For going to infinity all terms vanish except .
c) is also convergent regardless if you mean or .
d) is convergent because for positive n:
e) is definitely divergent because for positive n: .