MTH 1322 – Calculus II Homework 15 – The Ratio Test 1. Apply the ratio test to determine whether the series converges (absolutely) or diverges, or state that the ratio test is inconclusive. (a) ∞∑ n=1...

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MTH 1322 – Calculus II Homework 15 – The Ratio Test 1. Apply the ratio test to determine whether the series converges (absolutely) or diverges, or state that the ratio test is inconclusive. (a) ∞∑ n=1 (−1)n−1 n 2n (b) ∞∑ n=1 (−1)n−1 1 n2 (f) ∞∑ n=1 n! 22n (g) ∞∑ n=1 n2 (2n)! (i) ∞∑ n=1 n! nn Hint : You may use that lim n→∞ ( n+ 1 n )n = lim n→∞ ( 1 + 1 n )n = e.