MATH 1241: Calculus II A5-1 A5-2 Assignment 5 4. [15 marks] Assignment 5 (100 marks total) Determine whether the series is convergent or divergent. State the name of the Note: Give exact answers where possible (for example, It is exact but 3.142 is approximate). test used, and check that any conditions required for the test are satisfied. a. (5 marks) 1. [9 marks] 1 Ln( Inn ) 2 Determine whether the sequence converges or diverges. If it converges, find the n = 2 limit. b. (5 marks) a. (3 marks) 4n2 Zi Inn - In Inn an = n=3 1 - n2 c. (5 marks) b. (3 marks) V3n + n5 bn = 1+ 2 5" cos nn 1+(-5)" - n+ + 2n2 n=1 c. (3 marks) 3n)! an = 5. [10 marks] (3n + 3)! Show that the following series is convergent, and then approximate the sum accurately to four digits after the decimal point. 2. [8 marks] S(-1)n Write the number 22.563 as a ratio of integers in lowest terms. 4 3"n! 3. [15 marks] 6. [10 marks] Determine whether the series is convergent or divergent. If it is convergent, find the sum. Determine whether the series is convergent or divergent. a. (5 marks) a. (5 marks) 522 + 2n In! 7n nn n= 1 n=1 b. (5 marks) b. (5 marks) 7n 5n2 - 7 1572 + 2n n=1 1 + 3n + 9n2 (5 marks) 00 1 n = 3 n - 3n + 2 TRU Open Learning TRU Open Learning