a) Suppose that {ak} is a decreasing sequence of real numbers. Prove that if k=1 ak converges,

Question:

a) Suppose that {ak} is a decreasing sequence of real numbers. Prove that if ∑∞k=1 ak converges, then kak → 0 as k → ∞.
b) Let sn = ∑nk=1 (- l)k+l/k for n ∈ N. Prove that S2n is strictly increasing, S2n+1 is strictly decreasing, and s2n+1 - s2n → 0 as n → ∞.
c) Prove that part a) is false if decreasing is removed.