Question: a) Prove that if k=1 ak converges, then its partial sums sn are bounded. b) Show that the converse of part a) is false. Namely,

a) Prove that if ∑∞k=1 ak converges, then its partial sums sn are bounded.
b) Show that the converse of part a) is false. Namely, show that a series ∑∞k=1 ak may have bounded partial sums and still diverge.

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