MATH138 Study Guide - Final Guide: Ratio Test

• School: University of Waterloo
• Department: Mathematics
• Course: MATH138
• Professor: All

Document Summary

Ln ( + 1)2 ( +)2 = 2 = ( + 1)2 ln() ln()ln() =ln()ln(ln) As , ln(ln()) , thus eventually ln(ln()) > 2. Definition : a power series is a series of the form . Or ( ) =0 +1( ) +2( )2 . The domain of a power series is the set of such that the power series converges: no, it always converges at =center 0 0. ! = lim 1+1 || = 0 < 1 . lim +1 (+1)! Ex : what about ( 7) lim ( 1)+1 ( 7) = lim | 7| = | 7| < 1. So if | 7| < 1, i. e 6 < < 8, Series converges, also if | 7| > 1 the series diverges. If = 6 of = 8, check separately. Both diverge (geo, series or div test) domain is (6, 8) The interval of convergence is the domain of the power series.