1. (10.01 MC) n If the infinite series ) a, has nth partial sum S, for n 2 1, what is the sum of the series ) a ? (6 points) k=1 n - 1 k=1\f3. (10.02 MC) Which of the following series diverges? ( n+4 I. S n=1n- +n 1 II. S III. sinn TM 7=1 n2 O I only O Ill only O I and Ill only I, ll, and Ill4. (10.03 MC) 1 Which of the following statements about the convergence of the series is true? (6 points) 1= In(n+2) O Converges by comparison with 1 18 O Diverges by comparison with O Converges by comparison with O Diverges by comparison with 1=1n25. (10.04 MC) Which of the following series diverges? (6 points) Inn 7=3 n II. I (-9)7 n+2 7=3 3n Ill. E (-1)7 3 n=3 I only O Il only I and Ill only I, 1I, and Ill7. (10.04 HC) Do the following series converge absolutely, converge conditionally, or diverge? Explain your reasoning. Part A: (-1)" (5 points) Part B: (-1)"7 (5 points) (n+3)!6. (10.01, 10.02, 10.03 HC) 7 Let f be the function defined by f(x) = 2x-+x-6 Part A: Use partial fractions to evaluate [, f(x) dx, or show that the integral diverges. (7 points) Part B: Determine whether the series 7 M : converges or diverges. State the conditions used for determining convergence or divergence. k=3 2k-+k-6