142p23s11solution[1]

# V diverges constant multiple of the harmonic series

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Unformatted text preview: ate and interpret a suitable ratio. (R) Converges by the ratio test. (C) Diverges by a p-series comparison. (I) Converges by the integral test. a) b) ∞ n2 3n n n=1 n4 ∞ ln n n=1 n a) (R). The ratio an+1 an = n+1 3 n4 → 3 4 < 1. b) (C). For n > 3 ln n > 1 so the series diverges by comparison with the p-series with p = 1. ∞ 3n + 4n and en n=1 gives a valid reason? Circle your answer. No other reason required. 3.5 a) Which of the following correctly classiﬁes the series i) Diverges: limn→∞ an = 0. ii) Converges: sum of two convergent geometric series. iii) Converges: Comparison test with geometric series with ratio 3/e. MTH 142 Exam 3 Spr 2011 Practice Problem Solutions 3 iv) Converges: Comparison test with geometric series with ratio e/4. v) Diverges: constant multiple of the harmonic series. ∞ n3 and gives a 4 n=1 5 + n valid reason? Circle your answer. No other reason required. b) Which of the following correctly classiﬁes the series i) Diverges: limn→∞ an = 0. ii) Converges: Ratio test. iii) Converges: Comparison te...
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