Real Analysis Sequences Questions
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#1. Show that every sequence of real numbers contains either a monotonically increasing subsequence or a monotonically decreasing subsequence (or both).
#2. a) Let s_n be the sequence of real numbers de fined by s_1 = 1, and s_n+1 = (2s_n + 3)/4. For All n>=1, where s_1 denotes s subscript 1, etc.
b) Show that {s_n} is monotonic and bounded.
c) Evaluate lim s_n as n approaches infinity.
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This solution assists the student in solving calculus problems related to real analysis sequences.
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