hw7 - ∑ a n and ∑ b n to diverge but for ∑ a n b n to...

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CALCULUS 1501 WINTER 2010 HOMEWORK ASSIGNMENT 7. Due March 5. 7.1. Find the values of p for which the series is convergent: s n =2 1 n (ln n ) p . 7.2. Determine whether the series converges or diverges. (i) s n =1 n + 3 3 n 7 + n 2 + 1 (ii) s n =1 e 1 /n n (iii) s n =1 n ! n n 7.3. Show that if a n > 0 and a n is convergent, then ln(1 + a n ) is convergent. 7.4. Give an example that shows that it is possible for both
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Unformatted text preview: ∑ a n and ∑ b n to diverge, but for ∑ a n b n to converge. 7.5. If ∑ a n and ∑ b n are both convergent series with positive terms, is it true that ∑ a n b n is also convergent? Justify your answer. 1...
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