Let {A n } be a monotonically decreasing sequence ofreal numbers that converges

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Let {An} be a monotonically decreasing sequence ofreal numbers that converges to 0 and suppose thatAk (from k=1 to infinity) converges. a) Prove that the limit as k approaches infinity ofkAk = 0 b) Show by example that the result may be false for anarbitrary convergent series of positive terms. Let {An} be a monotonically decreasing sequence ofreal numbers that converges to 0 and suppose thatAk (from k=1 to infinity) converges. a) Prove that the limit as k approaches infinity ofkAk = 0 b) Show by example that the result may be false for anarbitrary convergent series of positive terms.

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