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chapter%208%20Appendix%20B

# chapter%208%20Appendix%20B - 3-1 M8 Supp\cmen'o...

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Unformatted text preview: 3-1 ' M8 Supp\cmen\'o.\ Mokcrial (AI’P‘3“‘\"m B) . I \ ' . Comment (see. RuA'mJ Fr‘mcipks o‘F Nakema‘ﬁcol. W6 E: A se%uence 0? real numbers {5n} {.3 said *0 Comm 2. *0 Q Vo\ue ‘0 W 'Fox. evend €>O Kev: eﬁs’s om ‘m’feser N suck Thai n2 N imphes _ I -b 4 e. '3 _ 5n \ 7;: Cauckg‘ Sequences . ’3'! . 3 A se\$uence 0“: reel num‘oevs {‘00} {s said *0 ,1: be a CNN“; geguengg H: For evevﬂ €>O There, Ta is an ‘m’teser N su c.\\ “mt "mmm ‘bn'Lm‘ ‘6 ‘* MN 2-. m“ (i) i: o. Seobuence 0F red numbets canvases "than it \s on. Quack se uence . (It) H~ a segueéce, oil reel numbegsﬁs'a Caucka " i'séguggqécéﬂg’in cw; ‘ PM? (a) IF “m bn=1> .Then For M3 e.» ﬁxere n-—>a> ms *5 on '\n\'e3er N “(1+ lbn-b|<e/z 15 MN Near) ~\ne%uu\‘\+j. ‘3’2 f: 32 2’ ' ’ i Eégagg lbn-kml s \bn-HHkm-H i; @335; K m) am; we 3' 3 . {\$343.5 H>n-\>ml<€/z+e/z=€ @Proof of Purl (ti) ‘\s 593006 “\e SCoPe Grins coutse 9i ConsiAer 0. se names of (ad numﬁets {En} Sn 5 B 5K K=I is ca.“ea ﬁx: a“ goﬁlo‘mm. The 'mﬁni‘h’. games on ‘ X 5K W“ 15 \$066 *0 converge ‘\:o 5 if and 0M3 H: lim Sn=s new (3.8., i-F and on FF “\e quhq‘ sums converge +0 9 Nﬂl‘ﬁﬁmm 303A ﬁ\\om\$ (mm We Cone)!» cﬁ’mion mo 5 ‘ ‘ he \\m L :0. ‘ . . a n 9.1. S \m 5 “ .oémdé‘" P m.“ DeF: Pmﬁseries of real nuan‘bug is said +0 com/erg: akso‘u’m‘y (1“ The series on 8-31 The—GE"): u: 2:5“ gomefses QBsaN’fc‘aA'hD Proof. 2 IF TM seats canvases a\>s°\u&e\x3 Wen ‘03 “we. CM¢\\3 ch’ferlq For 0:390 “\eve. dish an N suaﬁﬁu’t For mmz. N n X: < 6. K=m+\ {Sn} 333 Caudvsetbueﬂcc 04\$ \xence E7 5K muﬁ Conver e . =\ DJ: E ‘3K ‘93 soda 5to convefge uncondmonnuu w K=I 1F evaa re armngemcn" of 3s hms converges *0 ﬂ: same sum. ' exam \e Consiger ﬁn series M 00d one 0F Rs (Q amusements _ \ \ .. 0+é-‘-z)r<1z+%-¢)+<a+n-;)+-- L») ‘m which ’rwo posﬁive ’tetms ore abogs {mowed kg cm negosﬁve Jterm. H7 The. Sevies (ﬂconvefses {o s [Hun s < biz 1-5:; = 3 Let S; deno’m “w. n‘rh Forlﬁofl Sum oz" (3%)) HM we see “mi ' 33‘ <5; <sq < "' Q‘mce ' ‘ ‘ l 1- - —— > 0 4K3 LIK-l 2 K Hence .I‘F (its?) Canvases ’fo s' ,Hwn S. > SE:3 Héjig 5/6 s 1*- s' "meomm: cﬁ 5K Canvases ﬁnconéﬁiond‘d K=I - Li’ (ma ORB 'm if Canvases okAqu. Proof om i’i’red ...
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