Lesson 6.pdf - 6 Convergence of Sequences Sequences sequence as A sequence is a list of real numbers with a particular order We denote a(sn =(s1 s2 s3

Lesson 6.pdf - 6 Convergence of Sequences Sequences...

• Notes
• 10

This preview shows page 1 - 5 out of 10 pages.

6. Convergence of SequencesJuly 15, 2019SequencesAsequenceis a list of real numbers with a particular order.We denote asequence as(sn) = (s1, s2, s3, ..., sn, ...).Eachsnis called atermof this sequence.1[Example]There are several ways to describe a sequence as follows.1. Given the formula for all the terms, write down the sequence.(a)sn=1n. This is the sequence(sn) =1,12,13, ....(b)sn=n-1n. This is the sequence(sn) =0,12,23,34, ....(c)sn= (-1)nn2. This is the sequence
2. By giving the first few terms to establish a pattern, leaving it to you to find thefunction.(a) (sn) = (0,1,0,1,0,1,....). The pattern here is obvious. We can write it as (b) (sn) =2,52,3,4,2, .... What issn=?.sn=n2+ 1n.(c) (sn) = (2,4,8,16,32,....). What iss6? You can find 3. By a recursion formula. 51