Homework_Set_3 - Math 1a Fall 2005 HOMEWORK SET 3 DUE AT...

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Unformatted text preview: Math 1a Fall 2005 HOMEWORK SET 3 DUE AT NOON ON MONDAY, OCTOBER 17, 2005 (1) (2) (25 points) (25 points) Apostol, page 45, problems 11 and 12. Using the definition of the limit of sequences, prove that lim n→∞ n3 =1 (n + 1)3 (3) (50 points) Test the following for convergence or divergence but do not find the value. For convergent series, state whether the series is absolutely convergent. State clearly which test you are using: ∞ (a) n n+1 n=1 n3 2n n=1 ∞ 2 ∞ (b) (c) n=1 (−1)n n n+1 (d) 1 (−1)n √ n n=1 1 n(log n)2 n=2 ∞ ∞ (e) 1 ...
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