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Lecture 22

# MATH 0413 Lecture 22: math-0413-lecture-notes-22 Premium

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School
Department
Mathematics
Course
MATH 0413
Professor
Pan Yibiao
Semester
Spring

Description
02/15/17 - > Def CE K let { Xn3n° be a sequence and Le IR . ,, x we say That { Xn }n . , converges To L if The holds : bottoming ' + E E 0 , I RCE ) E IN SI . < IXN - LI E holds qon all n I k . In Thrs case we shall write win Un =L . n → when L EIR , we : That { xn } is a convergent say nai . sequence a x Kn l6 EXN } does not , we say That { Un n =\ converge }n . , is a . divergent sequence . let CCIR . Define { Xn } by = C t n E)N . { Un } Prove That to C . { Xn } converges t E 9 0 let N =L . , When nk nil we have , I Xn - Cl = 1C - cl = 0 < E Thus ihe limit C , converges to . 8¥ set Lx : C i.e. = Get order of elements [ 1,2 , 3) [3,2/1] ) : 1 Sequence under matters Cie . {1,2/3} F { 3/2 , } ) { = E IN ENI Define Xn } by Xn In t n . Phone That win in and win = O Xn exists 112 Xn . n → a had t E E 0 , wt k = I . when he R=l , we have - a =L 11h 01 llnl
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