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Calculus II Practice Exercises Integral Test Use the integral test to determine whether the series converges. ∞ 1 1) ∑ 8n n=1 A) converges ∞ 2) ∑ 7 n n=1 A) diverges ∞ 3) ∑ ∞ ∑ ∞ ∑ ∞ ∑ ∞ ∑ B) diverges cos 1/n n2 n=1 A) converges 7) B) converges 1 2n e - 1 n=1 A) converges 6) B) converges 1 2n - 1 n=1 A) diverges 5) B) converges 7 n n=1 A) diverges 4) B) diverges B) diverges 5n 2 n + 2 n=1 A) converges B) diverges Provide an appropriate response. 8) Which of the following is not a condition for applying the integral test to the sequence { a n }, where a n = f(n)? I. f(x) is everywhere positive II. f(x) is decreasing for x ≥ N III. f(x) is continuous for x ≥ N A) I only B) II only C) All of these are conditions for applying the integral test. D) III only 9) Which of the following statements is false? A) If a n and f(n) satisfy the requirements of the Integral Test, and if ∫ 1 ∫ ∞ f(x) dx. 1 B) The integral test does not apply to divergent sequences. ∞ 1 C) ∑ converges if p >1 and diverges if p ≤ 1. np n=1 ∞ 1 converges if p > 1. D) ∑ n(ln n)p n=2 ∞ ∞ f(x)dx converges, then ∑ n=1 a n = Answer Key Testname: 20_EX 1) 2) 3) 4) 5) 6) 7) 8) 9) A A A A A A B A A