So each problem is a true or false and should be either proven or a counterexample shown.
1) (I think I understand this one, but I am not super confident) If for all and is abs. convergent, then converges. I think this is false. If we use a_k = -1 and b_k = 0 we satisfiy our initial conditions but this implies that is divergent.
2) (this one I am lost on completely, I cannot figure out if it's true or false). Suppose . If , where < 1, then is abs. convergent.