MTH 1322 – Calculus II Homework 14 – Absolute and Conditional Convergence 1. Determine whether the series converges absolutely, conditionally, or not at all. (a) 1− 1 2 √ 2 + 1 3 √ 3 − 1 4 √ 4 + · · ·...

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MTH 1322 – Calculus II Homework 14 – Absolute and Conditional Convergence 1. Determine whether the series converges absolutely, conditionally, or not at all. (a) 1− 1 2 √ 2 + 1 3 √ 3 − 1 4 √ 4 + · · · (b) ∞∑ n=1 (−1)n−1 n 2n+ 1 (d) ∞∑ n=1 (−1)n−1 1√ n2 + 1 (e) ∞∑ n=0 (−1)n 1 2n (f) ∞∑ n=2 (−1)n 1 n lnn 2. Find an approximate value for the sum of the series that is correct to within 10−3. (b) ∞∑ n=0 (−1)n 1 (2n+ 1)!