3
Axaurs ts Renu 1 ' No. Tu ans J Nqdi-a Azt-r; ( tzozzed altf aeR q-q. = a , pmv€ that gf{}1.or a-= O or o'.= I ?.oo f : \--. at€ R ,nurroJnulr! q2 = a, qfeu dryt difuht c$n 4z=a <+ e'-a. =O. (+ q. (q -,) -- O cD) Tita dlasunsili"4n 4+O , harustoh Q-l=o qtau Qk,nvqlen dgn 4=l - kernudtor', jlka a+ t ha;:uslah a =0 Sho- *Lv+ there doeri't exrrf a raltonal nurnby t such*hql ?roof : And"1nn ada f e @. sehin rva'Lq + dpf drtulrt sQbaqqi =+ ,lrbez, b*o Akat\ letapi kt+a hacur rnencq"rt ni,rc,i a. gg tyllu^tnulo; 'lot, rnatwut aLgodlrnv Tembagrotl . tedapct 3 Lemwtal;.nz;,l , rqattu ,) a= 3n = q-a = 9m' 3la' ") 4= 3m+t -+ alL = grna+6m+l = z(grv.r, +zm) t- t :- 3'Y o" o) a= 3mta = AL = 9m'+l2m + 4 = 3 Brr:-. +4m+i) + 1 -; 3t o' unfuL s.dlqp m€t+u\o\ lyt?14v. gtq rrvnduW =,a" afldah a =3rn - Dureon den;l*tab. , daPat drfutrf bemUali a = 3m H a'-- gm' = 3bz a 3rrf =bz. ,3 3lb^ Kara-na "lb, , dgn ca-ra Ag sa-fia *p<roteh bhw zlb, Kqruq slq dant 3 lt *idak mwgh:n g'd b,[) = | shE

Tugas 1 Analisis Real (Nadia Azhari Alfiyyati 1202266) Latihan 2.1 Introduction To Real Analysis third edition

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Page 1: Tugas 1 Analisis Real (Nadia Azhari Alfiyyati 1202266) Latihan 2.1 Introduction To Real Analysis third edition

Axaurs ts Renu 1 ' No. Tu ans J

Nqdi-a Azt-r; ( tzozzedaltf aeR q-q. = a , pmv€ that gf{}1.or a-= O or o'.= I

?.oo f :

\--. at€ R ,nurroJnulr! q2 = a, qfeu dryt difuht c$n

4z=a <+ e'-a. =O.(+ q. (q -,) -- O cD)

Tita dlasunsili"4n 4+O , harustoh Q-l=o qtau Qk,nvqlen dgn

4=l - kernudtor', jlka a+ t ha;:uslah a =0

Sho- *Lv+ there doeri't exrrf a raltonal nurnby t such*hql

?roof :

And"1nn ada f e @. sehin rva'Lq + dpf drtulrtsQbaqqi =+ ,lrbez, b*o

Akat\ letapi kt+a hacur rnencq"rt ni,rc,i a. gg tyllu^tnulo; 'lot,rnatwut aLgodlrnv Tembagrotl . tedapct 3 Lemwtal;.nz;,l , rqattu

,) a= 3n = q-a = 9m' 3la'

") 4= 3m+t -+ alL = grna+6m+l

= z(grv.r, +zm) t- t :- 3'Y o"o) a= 3mta = AL = 9m'+l2m + 4

= 3 Brr:-. +4m+i) + 1 -; 3t o'

unfuL s.dlqp m€t+u\o\lyt?14v. gtq rrvnduW =,a" afldah a =3rn - Dureonden;l*tab. , daPat drfutrf bemUali

a = 3m H a'-- gm' = 3bz a 3rrf =bz. ,3 3lb^Kara-na "lb, , dgn ca-ra Ag sa-fia *p<roteh bhw zlb,Kqruq slq dant 3 lt *idak mwgh:n g'd b,[) = | shE

Page 2: Tugas 1 Analisis Real (Nadia Azhari Alfiyyati 1202266) Latihan 2.1 Introduction To Real Analysis third edition

ttda\- qda bltattqah ragsor.al t sden:irtna,,-r shq t"=3

kl q,b eR. and e *haf e >o Lu€ hzv< aS bteShouo that a<b?a.og ,

And,aLzn a>b . betarli a-b>o.Pilrt" e=Lh-a1 1, ,yv-ravq<btE = b+ *O-a = b+ -la ?

a>b + iq> \b shq d ditutis kem bqliagb+6 =)a+fu .*onla =40rpotole^ a 1a sl.B kon+ra};Lsi dgn fe.rnrlvta+t V g> obttalra a (btL. MaVq pzngandaiu\ gg banar aata.loil1V €>O dqn a(b+t btrlcfu 4< b

tf t1c ,showlhqt t<c<cz?rqqf ,Karer\a, clI + (c-t)70ka-rcra c2l dat t7o 4c srfd #arrs:lrif huloh't <>oShg c (c-r) >o =+ c"-c7 o + c" 7 c.

Ja8' k<tena c 7l datt C>c ,ttbutctt bqhwaI < c <cz

22ll[ 0.c<L , Show |haf cn < c {or all n €H ,q161 *hoiCq<c for n >L

Rqretla O<c<l bedalu.rBq.qran I ,

(;) unlut h=l b2nar , Sebafi C < <Gi Anaatuaa butar u1 n=k ,lqitu ck(c tlarus ditun-

Page 3: Tugas 1 Analisis Real (Nadia Azhari Alfiyyati 1202266) Latihan 2.1 Introduction To Real Analysis third edition

|.

- 711 '

k

da*t\<C c<l

i.Benzor UneH Eat D <e<l btlabt cn < c

01c < t + A(i) Untu1 rl = t benz^r

tii) Asumsil.z,,, b+tor u/ n=k ,A:att'u ck < c , k >- 2

flarrrSdl+uhJuLt-z.a benzr ul n=h+l ,k7r2ck+t ? ck. c

=( K+n cu <c Ban c <l,'. Jadi , botar Vrl € t"{ n ) I btrlabl en<c.