ECON211 Chapter 3,4: Chapter #3,4 Notes

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The text de nes a sequence as a function whose domain is the natural numbers {1, 2, 3, . (page 62). So if the range is n we could write the sequence as a countable subset of n. The limit of {ai} i=1 as i exists and is a n if for each > 0 there is some k (which depends on ) in the natural numbers such that. {ai} i=k n (a) . i , 3 + 1 i (cid:1)} i=1 is a sequence in 2 whose limit is (2, 3). A series, say {si} i=1 (not. N, n 2 ), with the structure that s1 = a1, s2 = a1 + a2, s3 = a1 + a2 + a3, and so on. If ai > 0 for each i and for i = 1, 2, . ai+1 ai. R where 0 < r < 1, then the answer is yes.

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