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1. Prove that if ak is a monotonic sequence and P∞
k=1ak converges, then lim
k→∞kak = 0.
(Hint: You may assume that all ak> 0 or ak < 0 (why?), then use the Cauchy criterion.
)
2. Rudin Chapter 3, 6abc.
3. Rudin Chapter 3, 11a.
(Hint: You may assume that limn→∞1+aan
n = 0 (why?). Show that an → 0. Then compare the series with an appropriate multiple of P an.)
4. Rudin Chapter 3, 14ab.
5. Salas 12.3: 12, 18, 23, 26, 28, 36.
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