Assignment 5 (100 marks total) Note: Give exact answers where possible (for example, it is exact but 3.142 is approximate). 1. [9 marks] Determine whether the sequence converges or diverges. If it converges, find the limit. a. (3 marks) = 4n2 an-1-n b. (3 marks) b = 1 + 5" cos x c. (3 marks) a = 2. [8 marks] 1+(-5)" (3n)! (3n+3)! Write the number 22.563 as a ratio of integers in lowest terms. 3. [15 marks] Determine whether the series is convergent or divergent. If it is convergent, find the sum. a. (5 marks) n=1 5+2 b. (5 marks) n=1 Ms Ms 712 5+2 c. (5 marks) 1 n - 3n+2 n=3 4. [15 marks] Determine whether the series is convergent or divergent. State the name of the test used, and check that any conditions required for the test are satisfied. a. (5 marks) n=2 1 n(Inn) b. (5 marks) 1 n=3 Inn-In Inn c. (5 marks) 00 3n+n n4 + 2n 5. [10 marks] Show that the following series is convergent, and then approximate the sum accurately to four digits after the decimal point. =1 (-1)" 3"n! 6. [10 marks] Determine whether the series is convergent or divergent. a. (5 marks) n=1 b. (5 marks) 00 5m-7 1+3n+9n2 72 n=1 7. [15 marks] Determine whether the series is absolutely convergent, conditionally convergent, or divergent. a. (5 marks) 00 (-1)=-1 n=1 b. (5 marks) C. 00 n=1 n (-1)+1 cos n 1+n (5 marks) 00 (-1) n=1 8. [18 marks] 1 n+n Find the radius of convergence and the interval of convergence for the series. a. (6 marks) n=1 5m b. (6 marks) n=1 (-1)"x2" (2n)! c. (6 marks) n=1 2"(x-2)" 4 +1