Sequences_Part2 - Subsecwence(oh/tn «cm-j sequence inn...

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Hwfi fwd: LnHH—L M111 ‘ So\u‘\"° OT. fl 5+1? h F“ MI, E max—.1 m Lmn\_—\=2‘.*‘=Z-‘=l- P=I So 5*n*emq.n\- is *rue. «For n:\- K 5*192: RSSva. *‘acfl' EPP\.= is *cug. 9:! 5L" 3: E 993-. "E m kuum =w+m —\ Hwnum , P31 9:1 :(Hn!tk+1+1)-\=U¢*133“ So *MQ S¥a*&m&n+ is "rt‘ue, $1M“ n:\<.¥‘- n Rance. h: ma¥MEMu~\'icq\ \nAUCHOf‘J pr\.=Lf\*\)\l-t )Vnétfl- P:\ E?“ Lefi‘ an BEL Aefihnaé °Q¢U°51VQA3 k3 o‘th an“ 241%“ - Show *Mafi' \Cm qn fixisi-S name m «ma m mac.- Show bogfiAQa, QBOVE' LiI' So\°'\“°“= F1r5+ usa. lnéuc-Han in Show 5.an is incrqafing. RSSQMQ. Qk*\7Q\" Then qk*1= J1*Qk*\ ‘? 1+qk =qk+\ V“- Now use inauéfio-n *0 SHOW Echo) {S BounAQA Q‘bove 53 A. Q\=\L4 ' Q55.me QM 4. Ly- The.“ chm: \IHOLk 4 2H. :J? 4.4 59, «(‘44 V0. Quark: I {an} 3'5 an PosH-WQ saqunLQ- So, {an} {I \yaunAaA \OQ.\¢w ‘35 0- .21qu :5 LounAaé- SWHLC. EON-13 :5 \znunAeA aha Mono¥00§cj :3“ :5 LOnVflP31n*o fi-voo “Then L: “m Qfia.‘ =. Um JL‘V'Q," -.= \] 1-H- ‘fim fin = \lz-n-L n-yda “'5‘” fi-‘roo 5°, fink—2:0 E?- J 1.1..A-k-k-4A ..\"3. -74—2 Since. {an} is PosH-Tve,\~°- know \‘m qnyo. fi-‘vm So , 1.7-2 . 3-8.. Um Qn:'1_ . n-wcn MEHMETONURFEN METUDEPTOEIMTH. RESEARCH ASSISTANT 0 Ex: snow Hufi 11m Lu: n-wa M. So\o"r:t}nt n n. 7“ - L.3—_-_7.-._-—-3:_ ALL—.L-L x¥ n73. m ‘ N 1 3 n * 1 3 3 - \___...-——-___.---'--J n—‘L 41-1sz 0 z “‘1 _ So, \{3 073 n\_ n 1 “'3' ~ 1—:0. We. know freq =0 :50 ‘05 Sammie. +\~e.are.m M n «L n—3 ‘ 3:.— 4 2 v\'\-\Ma\*?—‘3. Ex: FKnA final-\- 9-? “PM. Steinem-2e. ianc¥ankHfiNK~ Suki-1cm: Le-‘t- Qfi: “Chef—*‘qn \tln‘] an $Lx): xqvc*antlxj. _.——-——— Then Qn:-?Ln\, anti \‘wn Qn = \im {:tx‘). n—ym 78-900 0 )k-‘roa “'500 ya,“ “1‘ K (.I ‘ W ' ‘— I L“ . HUM)" K'- _ _ = 1‘ Z hm ____-———-';'—"‘"'_ .. 'hm —--—'——""‘ 1 x500 flaw t-x-[T] K 5°, 9-300 . h 'L “ EX: F‘ufiA \n—n K‘fi' - fl “and: u. n * s.\o+.on: La a”,ng ma ¥Lxu=h+3§¢j . Sofia—ALM- \im fix]: ex? limb; 1n\\+3-;3) : a“) “m ln\\¥1h£') x-aao Inna *4,“ “x 1 ‘ .(‘2‘ L“ - H-z/x T = Wm * fifim '-—' x4900 \fi-P; X1 x 5 0 Qn=QL. (II-50° X1 Show +\-\c\+ “m 02111:,“ CV“; “m an-HzL 1*‘1lfl {an} is “'_ name flaw Convaogzni‘ and 13m “n = L.- fl+m (H: igfll=iq\;q1rq33q¢11"'} J‘V‘e'“ iqzn1=iqlzqq:qe,u-3 Gina {Q10H111C1Lq5’q—frflz not +wo SuESLc‘uanas 01F Eqnz.) w LL‘P E70 be taxman. Our aim \‘5 *1: show *Me-ol efiisars N=NL&) S-‘L $00 L“. n‘7N wQ \nQVQ \qn-‘LL‘ia‘ 5"th Um qaniL; 3N1 S-“‘- H? nabh we. have. lqzn—L\4£. fl—I’og SJmi’mc-IL since. “m Q1n*‘=L—;3N1 5"“ U? “‘7 N1 “'9- VWNE \q;n+\‘\-—\'<En fl-‘roo LeA- N: qu £1N1J1N1+l3. 1) H: n u cyan, EMEZt 5.4L nzlm- 5a,. $0? nvN (Wanna. n‘er1qko) we. have. \Qn-L\=\qu-L\‘C ° 1m: n n oea, Ewan" :.+, nzlfllfl’" 5mg“? n7“ (Man n>1NL+{,qnd 3:; k‘rNt) we. \MWL \Qn~L\:\Q1k*\-L\‘& .‘. Vn'rN we. Mauve. \Qn-L\4E. c’. q“: L- "‘50:: \ x x x \_ L _\_ __ Ex: Ogfi-gcmzng wh&*‘hQ.f' *Me. sequence. {h-YITJ '2': 3J 5 " A ’ (a ' Converges or {Liver-3&3. H: 1": mavet‘gts , $in$ H-s “Mi-k . l So\u‘\-\on: 0&1“: ‘ qné q10*\ : n+1 n+l “m ‘11“ = “m an“ : o . T‘napfiont , {an} is convec‘39.n* cum! \§m°-n= 0' Ex: therm'me. wN-‘Mrhar \"Vfl‘. sequtncfi. £0, l, 0,0, l; 0,0,9, {1 “-2 convaoggs ar‘ Aivaraas. Solui‘ion: 11ml : {0, o, O, "-1 tuna [in] ‘: [LL—"p"? are. Subseguances o-Cia1:10l,o,o,i.0,o.0,h--~Z-“HA3:\:M‘°n=° “‘5 “m cnzl' nae-u fl-Imo Sa ion} is Alvet‘gecfl since H has *wa Su‘nfilqulflcts “5H” 3:9pa'°"* “man. EA: F305 \zm'd- 0’? 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This note was uploaded on 05/09/2010 for the course MATHEMATIC 120 taught by Professor A during the Spring '10 term at Middle East Technical University.

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Sequences_Part2 - Subsecwence(oh/tn «cm-j sequence inn...

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