9.2 - “mmfifij ....QQW.Jfi/£s, _ _ J b A series is Sam...

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Unformatted text preview: “mmfifij ....QQW.Jfi/£s, _ _ J b A series is Sam l "2/ wah For a geomefm‘o Ste/716$ a” = ax”" K. ,4 loan/2d sum ) 5‘”) is #76 fimjv : n—Terms 014 a series 81’) — Z ac n=1 4 Seauenca )5 4 57101173 07¢» numbeflé. /5 Convergence are Seawences I‘ The pawl] sums 79/074 seam/mm SUSZDNOSnwo ,“Tha- SQGzUQflCé has a. [ma/f , L, Cur/7739’? “KL/’3’) Sn : L, W00 Z‘F // I s , ‘ “:30 in L €XISTS 3 5m Ala/766 60/7 1/6526. 1 ofiygm/zse) 5%06/766 d1 Vegas. I {,Two Useful leHs m x” :0 136 mo héflo Jain J_—_-O [4'700 ’7 z—TS TS 260 SHE E L p w I»... LU IJJ. II mm cc mo ,. vw v¢ x—P si‘ch (\‘N g Q £0an é ,‘Examéie’l F/rid Hm, Inn/7 0F same/Ice, J 710 fr‘exzsfi‘ iii! = 3n Wojwmpare, [Mo 3” wth (/m’vx", Hm), /5/7/So r7700 moo : W5 W9“ ' ~n 2&2, 5n __ l — e : /+e‘“ mm M Mn N = 10’?) e“’)"-— o n~7m new T _I [e /</ ; W, Jim 2 l I W moo Sn W 8. Sn ‘3 /+ (*l)" W [—/)”:/ when nsevm) bur =0 tum/'1 '7’)=§dd. 7100’2750760 51:03 $232, 5530. and 7797b 526200766 W53. 9‘" JP "4’- x A‘ Theorem Convergence, 0% an IncreasngWL/nded Seaweme 115 a Secéuence Sn flCa-r nzlglfinu 375 increasfng and bounded alcove,fl2en £1425)? exisfls‘, as K r‘l r t 5 PI Qonverqence, 9P. “éegzuezzcggwmihs __ ,_.‘, 50 SHEETS 22442 100 SHEETS 22-144 200 SHEETS 22—141 . \\ Cm \ A NWA 0/ a // A15 ‘ ! Convemence, 0F Sen F ' 00 IF lImSn = S , than we say #26 semes Zan n~70<2 ha, convemes and flow rrs Sam is 8. IF fine Mm? #003 nor exzsn we, say Hm genes dim/276$. In words: .129 imam/9am +976 Converqente 05 a, serxes. fan , we faked, faok gr) firm secgueme, 05 T7926 pam‘a/ sums 3;,52,m,5n. J6» 5n has a, 0277/? as 77~700 then find- Mn}? is fine sum 01A We, series; Theorem: Oonw ence, PM (77163014 Series 1, IF Zan é) an Convequ 4% FF k is a Carma/77L than E Z (ax—Max) Converqes 70 fan 7‘ Zén Z kan Converqu “tn KZan J i {3. Changing a fi'nfre, # 01’? Terms in a 56MB does 790+ change whether or rm 'IT conve as al+hou b H mm Chan 46, m ( SW19 [+177 00 vemesq ) t ' ‘ r ~ ‘5 IF 2% Convemesj wman ~O (( $12326 (Jr/$11M?) 4.1% fan dwevqes3 may, Zkan Moms 1? («£20, . l Mdhfiiicamevqm 01C SEQQW (£3 (E Series E VISUOJIZCFCIOH OP Senes For an7/O W), We Can Visuallie fine, SQWS as recfangles wi’rh an mm 01” “an” (base: 1D 50 SHEETS 2441 22442 1.00 SHEETS 22—144 230 SHEETS The series converqeg “IF 7%, ma am 041 Vecmmgles is Purine. 2 m-Tr‘nn/ \_ w r u \‘ Aj/ 00 Th6 ‘is SImIIaV To lmwaper mfgm) foMIX where am Can ba 6mm even 0 Wow/0h RS on an mfinm Wen/a}! Compavzsan 0F Sevias (Q Inteng i We, [May/a! Test Suppose, 030 and fix) w is 0L decreasmg pasmVQ Funaion defined far an xv/C Lulflo an: H10) V0. 00 o H SQ 4%de converges) finer) Zan convmeS. A o If I: Pc><>d7< dwerqes) Wm 206m WW6. 22441 50 SHEETS 22-142 100 SHEETS 22-144 200 SHEETS AMFL / Show ‘Jrha Series 5* sums mufi Tend in . a 3 ) (IV; 7.5”} " 310,000 8 )000 > Moo 3. I? ZanwflV) wen haw- Con‘wmence ofJSQaumces 1Q Saks 1+ —‘-+ J—+H l 3 . dwemeg This Is coule firm harmomc semés. To Converge, fihe, SQSLUQYZCZ, OP parha] CL hm'hfi Szoo *5 5o )6]; %Ci.?°}. «2 Mn La baa) 5: X x b ‘3- «elm DWIX‘ In E9709 03 = Ju'm me- ' b—700 [ s.— Jum (Mb) dwmqgg 10-900 I? you Comma WY) an 3 Mn :0 V1900 aou‘M see/ how Thad" fluid propen} Com? be used In Opposma mom WY) 60130 it” slow D bu+ \‘H’s growng wlfimuf bound. ETS SHEETS S!) SHE MO 200 SHEETS 22142 22.141 / 22—144 /’Z§f\ / V \x \A 9 n rm n/ E I Show fi ynp Convemes <19r p71. g n1, ’ 00 aCompam UUI‘H') flue, InngraJ f0 (7X9)d><. ‘For pailD we, have; b 00 r L y -F+l / fl X’pdxcltm J-pdxrlém [3%,] , b~7m / X b~700 ':. ... L by“) I'P 1"? , To evaluaqte +1013 1mm?) we, mu3+ Congloler‘ p7] @ Pd. p71 Power 0F b Is heyaflvebm hm]? axzsfrseflws E +he/ mTegml Corn/ewes go 80 The, Series Conques. ? power 0% b is Posmveaso hmTT "DIVE. Thug The, 1n+e9val dwemng so Hoe, S€PT€S dWQV‘QQS, ‘06 0122’ Him with WRVJOMS exampIeDWe, «. hwmvmc Series dxve-rqas. . file/Cy, ...
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9.2 - “mmfifij ....QQW.Jfi/£s, _ _ J b A series is Sam...

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