MATH 1ZB3 Lecture 10: 11.8 Power Series
20 Feb 2019
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Infinite oprodffnomialf if cis thesame thiscarouldbe ageometri series a series withthe form. I usuallystartfrom0 u. tl where each cnis a constant in x variable inn he assumes. Tn u x isin theseriesasunknown power series are functions of x anditsdomainis thesetofall suchthatseriesconverges. Thi eg zo a. pl n couldbeaproblemwhenao sowejustdropthet 6m iotest aanni powerseries c thxin theconstant sidenote terms h hasnothingtodowith1kfunctions. 0 noshift f itis a proximationofits derivativesyoujustdroppedthispower a. 1. 1 44 therefore ix ale a rs x. R radiusofconvergence a112 f g ratiotest find whenratio lime centerof vergeng. It a n a 1k i tinea e intervaloftonnage"re endpoint. Eg if n5 z that a kowon 1point seriesconvergeswhen. Seriesconvergesforallteal tea a vet rsuohthatyseries x dn find radius center andintervalof contonto always cow hhal. E d provenguv atk x e it"s s i ie xeff. es l in nu w h h4 an112 tix it. I a f xa es a x dir. Is i x is t. ee x ilu eosxcii n t 2.
