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Day 26 & 27

Day 26 & 27 - pp 00 2 a n(X-c n;o i~ Qn(X-c:JY Q =...

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+ Q 3 Cit - c.') + \ " a h LX - c.., ') -+- I I I 50) given 0.. power series J we pp. 2: 00 an (X-c.)'" i~ 0 .... pow€/r ..serie.s n;o wi h. c..&n-teA' C- £ 00 Q (X-c.:JY) = 0. +-0..1 LX-~) + Q.;2.LX-e-}J... n 0 -n~O 3 ,.., W'l LL ~ i nd -t:h e do rnO-i n (ra.d 1 uS o.nd intervaL of C£Jhver<jence'J.
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r- S;-hw.i:ion ~ 1-::: 0 u.s;n5 the. J(aholcsi 00 n ("Y);'l CJ.!.. . <:I ( I)n Cx-~) X-pt~ - ~ ~ 3' 11\ Q~\~3'3n(y\+\)~ ~ ~_~"'"'i+-B~ K'T) ~ (x- 0(X.- ~n n t. 3 n ) < l n~oo 3.3Y'\(n+1Jn~ LX-~)n ~~ -- ___ -needs -to be. -l::ru..e. ~r Co'nve.x-gBrlc.e.. ~1 CX-~)~ ¢/ « I Y1 ~ 00 3- T(n+-~ ~,~~~~_----=-===~_ ~l (x-~) <:::: 1 ~ \x-~1U-nu I .. < 1 'Y\~DQ 3(n+\1 3 h-)oo jBCn+i) S \Y\e.e ~- 1 == 0) then -tor 0 h-700 3CV"\+lJ /} Qnu X; L~ IRl) \x-::{\~ I < 1 ""d h-4l>Q (n+() clovnci\ n \ :s all?l t c.erd:-er '1 S ~ eX - ~ ') 'ro.dlu.s \s \n+;'Y\t-te
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-=---=-=~p-----~ 00 -=,-~~f;l- ~ II ~ (a x- \'(' 8 ~ RT \ (D+\)/ (dX-1J (;;) < 1 ±Or:~~-----, ~ ('I v ~ t)_~= ---~J~~~ ~---H-- -----l~ n ~ co . ~,. -- -- Can'J ec-s CaJ ~ 1---_--H-\~X-\1 ~(rl+l) « 1 '(\~bO S \~C e.., ~ en + \J := ()<:::) --thev-~ i.s h~co -
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So) c.,~::L --1+ -I:::b Si-tu..o:t-leQY) ~ :_ L ~ 0 and ~ ~ '-t:e U-S\YI<j ~~o Tes-t:: ~=" ---H 1 -- ..... - ~- r.:::.3 ! --H- 60- need -t:o c}.eek e.nd poi n-t-.s --0- 5" e e.. , ~ 'i::h e:J a:, e , Y\ e.-l u..d e..ct . .. ~
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A -t. x = .5} eX. - :J. J 'R == C 5 - d '/~ :=: 3 k-;-==--_ '-, _ oa 00 1 So +Or ~ :.R == ~ *- +hoi cl \'\leA-fjes) ~= \ J So 'X. -=5 is N OJ ~~_ elY) -eh e. doyna-l h So deYY'"\o..in \5 : c:=f D -\~ X.c::S * On \~ 'i\e.ed. -to 6hou.,:) e..Dv\veY""csenc..e.../ hat e,c.: 0, c, ~
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])I oin-h'CJYl Kev i e0..J ~~~=~==1=~-~~-- ~n n-~ ==- d~ hi. ~ \ (~n ') I I ~--=-----t1~-=",-,-,d Y\ \ == .;? Lh (n - I) · · · d' I J-,~.-------~-~-~ ~ = (~OJCdn-l)C~y:)-dJ'" 3-~·J_ _~=~C~n yr) ==- (';;;l~)n == d:;)n or d "cdr) '::::dh~n
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