Question: a) Suppose that {ak} is a decreasing sequence of real numbers. Prove that if k=1 ak converges, then kak 0 as k .
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.
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.
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a Since the a k s are decreasing ka 2k a 2k a 2k a k1 a k2 a 2k 2k jk1 a j ... View full answer
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