and the series 2 ) п? 1. For all n п > 2, n3–5 converges, so by the Comparison Test, n2 the series > п converges. п3—5 arctan(n) and the series :2 converges, so by the Comparison 2. For all n > 1, n3 n3 2n3 arctan(n) Test, the series >) converges. n3 In(n) 3. For all n > 2, , and the series E- diverges, so by the Comparison Test, the п п In(n) diverges. series E 2, and the series 2 >- diverges, so by the Comparison Test, 4. For all n > 1, n In(n) the series > n In(n) diverges. In(n) 5. For all n> 2, n2 and the series >, n2 | converges, so by the Comparison Test, п2 In(n) the series > converges. n2 6. For all n> 1, and the series > n2 п converges, so by the Comparison Test, 3-n3 n2 the series > 3-n3 converges.

and the series 2 ) п? 1. For all n п > 2, n3–5 converges, so by the Comparison Test, n2 the series > п converges. п3—5 arctan(n) and the series :2 converges, so by the Comparison 2. For all n > 1, n3 n3 2n3 arctan(n) Test, the series >) converges. n3 In(n) 3. For all n > 2, , and the series E- diverges, so by the Comparison Test, the п п In(n) diverges. series E 2, and the series 2 >- diverges, so by the Comparison Test, 4. For all n > 1, n In(n) the series > n In(n) diverges. In(n) 5. For all n> 2, n2 and the series >, n2 | converges, so by the Comparison Test, п2 In(n) the series > converges. n2 6. For all n> 1, and the series > n2 п converges, so by the Comparison Test, 3-n3 n2 the series > 3-n3 converges.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 41E

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