MATH 137- Final Exam Guide - Comprehensive Notes for the exam ( 104 pages long!)

• School: University of Waterloo
• Department: Mathematics
• Course: MATH137
• Professor: Jun Liu

Document Summary

Chapter 1: arithmetic parts for limits of sequence. Chapter 1: introduction to series: a geometric series and the divergence. |(cid:1876) 0| measure the distance of (cid:1876) from the origin. |(cid:1832) (cid:1833)| (cid:1877) (cid:1877) (cid:1876) (cid:1878) (cid:1876) (cid:1878) for < case for = case. Inequalities: triangle inequality i e. g. (cid:1832)((cid:1876)) is a height (cid:1833)((cid:1876)) is the height of a plane. Equality if (cid:1878) is between (cid:1876) and (cid:1877) or (cid:1878) =(cid:1876) or (cid:1876) =(cid:1877) |(cid:1854) (cid:1844)|(=)(cid:1876) ( ,(cid:1853) (cid:1854)) (cid:1876) ((cid:1853) +(cid:1854), ) (cid:1876) = 2 ( (cid:1876)(cid:2870) = 4. |(cid:1876) (cid:1853)| >(cid:1854) (cid:1876) = 2 => (cid:1876)(cid:2870) = 4. So, (cid:1876) = 2( ) (cid:1876)(cid:2870) = 4 (cid:1853)(cid:2869), (cid:1853)(cid:2870),(cid:1853)(cid:2871), . (cid:1853) (cid:1853) denotes a term. If we have a general formulae then we can write it. A sequence is an ordered list of numbers, in this course usually infinite. (cid:1853) (cid:1854) (cid:1853) (cid:1853) +(cid:1854)