Homework 2 Solutions- Infinite Series - Matthew Choi...

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Matthew Choi Math6B-01-W15-CHEN Assignment HW2 due 01/22/2015 at 11:59pm PST 1. (1 pt) Determine whether the sequence a n = 1 1 n 2 + 2 1 n 2 + ··· + n 1 n 2 converges or diverges. If it converges, find the limit. Converges (y/n): Limit (if it exists, blank otherwise):
2. (1 pt) Find the limit of the sequence a n = ( cos n ) 3. (1 pt) Determine whether the sequences are increasing, decreasing, or not monotonic. If increasing, enter I as your an-
swer. If decreasing, enter D as your answer. If not monotonic, enter N as your answer. 1. a n = n - 4 n + 4 2. a n = 1 4 n + 6 3. a n = n + 4 6 n + 4 4. a n = cos n 4 n
4. (1 pt) Suppose a 1 = 1 2 - 1 2 , a 2 = 2 3 - 1 3 , a 3 = 3 4 - 1 4 , a 4 = 4 5 - 1 5 , a 5 = 5 6 - 1 6 . a) Find an explicit formula for a n : . b) Determine whether the sequence is convergent or diver- gent: . (Enter ”convergent” or ”divergent” as appropriate.) c) If it converges, find lim n a n = .