Lesson_15 - 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 15...

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Unformatted text preview: 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 15 lebxz crlb oxr :dkixr oxia xnr ,cwy inrp x"c ,ipinipa a`ei 'text :ddbd uixw di`n :dqtcd zewfg ixeh 1 xy`k , ∞ X n =0 f n ( x ) zeivwpet xeh ly ihxt dxwn `ed ∞ X n =0 a n ( x- x ) n zewfg xeh . f n ( x ) = a n ( x- x ) n :dxrd xehd zetqep zecewp dfi`a zrcl dvxp . a my enekqe x = x dcewpa qpkzn zewfg xeh lk yxetna oiivp ok m` `l`) ∞ X n =0 a n x n dxevdn mixeha weqrp xnelk , x = 0 gipp eiykrn .qpkzn .illk x-l mitwz mihtynd lk j` ,(zxg` 1 htyn hlgda qpkzn xehdy jk (xehd ly zeqpkzdd qeicx) R ≥ miiw ∞ X n =0 a n x n zewfg xeh lkl ∞ X n =0 a n x n 1 ixtqnd xehd , | x 1 | > R-y jk x 1 lkl . (- R, R )-l iwlgy xebq rhw lka deey dcinae .xcazn :dxrd . R-a x lkl qpkzn xehd R = ∞ m` . x = 0 xear wx qpkzn xehd R = 0 m` .` ici-lr x =- R-e x = R dvwd zecewpa dxew dn xxal jixv , < R < ∞ xy`k .a .dxiyi dwica :xncd-iyew htyn . R = 1 lim sup n →∞ n p | a n | i"r oezp zeqpkzdd qeicx .zewfg xeh ∞ X n =0 a n x n idi :xan`lc htyn miiw dfd leabd m` , R = lim n →∞ a n a n +1 i"r oezp zeqpkzdd qeicx .zewfg xeh ∞ X n =0 a n x n idi .(agxd oaena) 1 1 libxz . ∞ X n =1 x n n xehd ly zeqpkzdd megze zeqpkzd qeicx z` e`vn :oexzt . a n = 1 n o`k lim n →∞ 1 n 1 n +1 = 1 . R = 1 okle :zeevwd z` wecap .xcazn `ed ik xak epgkede ,ipenxd xeh edf ∞ X n =1 1 n : x = 1 aivp .uipaiil itl qpkzn xeh edf ∞ X n =1 (- 1) n · 1 n : x =- 1 aivp . [- 1 , 1) `ed zeqpkzdd megz ,okl 2 libxz ∞ X n =1 3 n + (- 2) n n · ( x + 1) n xehd ly zeqpkzdd megze zeqpkzd qeicx z` e`vn :oexzt lim...
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This note was uploaded on 03/12/2011 for the course MATH 104010 taught by Professor Dr.miriambarazinna during the Winter '11 term at Technion.

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Lesson_15 - 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 15...

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