Determine whether the following statements are true and give an explanation or counterexample.

a. A series that converges must converge absolutely.

b. A series that converges absolutely must converge.

c. A series that converges conditionally must converge. 

d. If ∑a_k diverges, then ∑|a_k| diverges.
e. If ∑a²_k converges, then ∑a_k converges.
f. If a_k > 0 and ∑a_k converges, then ∑a²_k converges.
g. If ∑a_k converges conditionally, then ∑|a_k| diverges.