Calculus 1000A/B Lecture 5: seq
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21 Jan 2019
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CALC 1000A/B Full Course Notes
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A sequence s is a function s : n r. it can be thought of as a list of numbers s1, s2, s3, . where sn = s(n) for n n. Example 4. 1. (i) {sn} =(cid:8)1, 1 (ii) let. The corresponding function s : n r is given by s(n) = 1 n . Example 4. 3. s1 = 2, sn =p2 + sn 1 for n > 1. Then s1 = 2, s2 =q2 + 2, s3 =r2 +q2 + 2, s4 =s2 +r2 +q2 + 2, . A sequence {sn} converges to a real number l if for every positive number , there exists an n n such that |sn l| < for all n > n . If {sn} does not converge, it is said to diverge. sn = l. 1the fibonacci sequence is named after leonardo of pisa, who was known as fibonacci (a contraction of lius.