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Chapter 9 1 1 2 n 1 n Does converge or diverge and why? 2 n2 n 1 3n Does converge or diverge and why? 3 sin n 5 n 1 n Does converge or diverge and why? 4 1 (1) 3 n 2 n 1 Does converge or diverge and why? n 5 1 (1) n 4 n 1 Does converge or diverge and why? n 6 2 n 1 3 n Does converge or diverge and why? 7 How can you tell if a series is alternating? 8 When proving an alternating series converges, you first should… 9 You have shown an alternating series does not converge absolutely, how do you show it converges conditionally? 10 When is it a good time to use the root test? 11 How do you prove a series converges with the root test? 12 How do you know if a p-series diverges? 13 If you want to prove a series converges using the direct comparison test you must… 14 The limit comparison test can prove a series is a convergent series if … 15 When is it a good time to use the RATIO test? What must happen for a series to converge using this test? 16 How do you find the Interval of Convergence of an infinite series? 17 How do you find a Taylor polynomial approximation around x = 0? 18 What is the general term of the Taylor series centered around zero for 2x f ( x) e What are the first four terms of the Taylor series centered around zero for 1 f ( x) 1 x 20 What is the general term of the Taylor series centered around zero for f ( x) cos x 21 State the first four terms of the Taylor series centered around zero for 2 f ( x) sin x 22 What is the general term of the Taylor series centered around zero for 1 f ( x) 1 x 23