02/15/17
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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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