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midterm Second exam - 140A Solutions March, 5. 2007 1 Exercise 1 (25 points) s2 +1 n 2. Let us consider the sequence (sn ) for n N dened as s1 = 2 and sn+1 = (10 points) Assuming lim sn = s exists. Show that s = 1. (10 points) Show that sn is non-decreasing. (5 points) Does the limit of the sequence actually exist ? (explain why) Solution: Let lim sn = s exists. Therefore lim s2 = s2 and n lim sn+1 = lim...
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midterm Second exam - 140A Solutions March, 5. 2007
1
Exercise 1 (25 points)
s2 +1 n 2.
Let us consider the sequence (sn ) for n N dened as s1 = 2 and sn+1 = (10 points) Assuming lim sn = s exists. Show that s = 1. (10 points) Show that sn is non-decreasing.
(5 points) Does the limit of the sequence actually exist ? (explain why) Solution: Let lim sn = s exists. Therefore lim s2 = s2 and n lim sn+1 = lim Solving for s leads to s = 1. Let us compute sn+1 sn sn+1 sn = s2...
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