073 A E Ant Ita
Ca prove by induction that it's increasing thenshow thatit's bounded
let plk AlecAkil e KEIN
Basecore KY Ai J2 Az JIE
A2 2 Az2 21To A
Az a and a 0 AzO
as Ai
so pus is true
Inductionstep Assumepus is true Akcake
As akti JFAK tak akh 2 yfgpuysplktyHIIZTI.FI 95858k
SO Alai 2cake from piksB tree IDEHFB.YIAKy
cwt.si 2CktDDtve i.e.AkLAkI2where Akt i
Akt c 21Aki
Aktic Ital
AKACAktz
pika B true
So plk pilot is the for all KEIN
Go by PML pin is true for all new
So cann B increasing sequence
As it is increasing then AnCIN An At 52
Also Ant Tta An42 2 tan an Cas anti an E 07
an an 2co
can 2 anti O
I can 2
theEIN and an is boundedaboveby 2
land is bounded aboveby anynumber largerthan 2
awe
thereforeboundedby3
As au is boundedVandincreasing thefm it is convergent
let finan L
flyan LIYE anti 2 GHanti 2 An 2
L L2 2
L2 L 2 0
L27cL117 0
1 2 or 1 1
as THEIN an352 2 2 is onlypossiblecase
Afar 2
Qy5 91 3 An Elani 15 n 2,3 4
why increasing An2Show it's increasing by induction as a3 45condition pin An Anti NEIN 944.75
base Case n 1 Ai 3 Az Ica 15 2 3 5 4 Seethe 9pattern
Induction
step
Assumeplk is the KAN
p 90 Ak
C9ktI
want toshowAk4 94 2
aka LEcakti1571
As Ak4 12AK157 Ak 29kt 5
SO AKLAKH Zaky 5SAKTI
aka 5
Zaki c E
aktl zakyczf.itThivan to show
AKA LILAH15
aka Lake 171kt is the
so 1744 pike for all KEIN
By P.M I plus is thefor all new
So can n is increasing
SO VnelN Anti An Ilan 15 an
an 15 2 2am
5 an
an 5 cann is boundedabove
As can is increasing boundedabovethen by Theorem4.2 it's convergent
hat hekinfoan
so ftp.an liygzcani 5 3 Ehsan1E

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