Give an example of each or explain why the request is impossible referencing the proper theorem(s).
(a) Two series Pxn and Pyn that both diverge but where Pxnyn converges.
(b) A convergent series Pxn and a bounded sequence (yn) such that Pxnyn diverges.
(c) Two sequences (xn) and (yn) where Pxn and P(xn + yn) both converge but Pyn diverges.
(d) A sequence (xn) satisfying 0 ≤ xn ≤ 1/n where P(−1)^nxn diverges.