Lesson_5 - 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 5 lebxz...

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Unformatted text preview: 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 5 lebxz crlb oxr :dkixr oxia xnr ,cwy inrp x"c ,ipinipa a`ei 'text :ddbd uixw di`n :dqtcd :zexrd , L leabl miqpkzny mixtqn zxcq { a n } ∞ n =1 `dz .1 . L leabl `id mb zqpkzn b n = a 1 + a 2 + ... + a n n zipeaygd mirvennd zxcq if` zqpkzn C n = n √ a 1 · a 2 ...a n zixhne`bd mirvennd zxcq mb ziaeig dxcq { a n } m`e . L leabl ( .dgked `ll :lbxznl ) . n √ a n n →∞----→ q f` a n +1 a n n →∞----→ q m` ik gked .ziaeig dxcq { a n } ∞ n =1 `dz .2 xiaqdl :lbxznl n √ a n = n r a n a n- 1 · a n- 1 a n- 2 ... a 2 a 1 · a 1 1 n →∞----→ q . lim n →∞ n √ n ! n :ayg 1 libxz :oexzt n √ n ! n = n r n ! n n . lim n →∞ n √ a n = 1 e mb diipyd dxrdd itl f`e lim n →∞ a n +1 a n = 1 e-y d`xp . a n = n ! n n xicbp a n +1 a n = ( n + 1)! ( n + 1) n +1 · n n n ! = 1 1 + 1 n n n →∞----→ 1 e :htyn .dly menxteql zqpkzn dneqge dler zipehepen dxcq • .dly menitpi`l zqpkzn dneqge zcxei zipehepen dxcq • 1 2 libxz :oezp a 1 = 0 a n +1 = 1 2 p a 2 n + 12 n = 1 , 2 ,... .dleab z` `vne zqpkzn dxcqd ik gked :oexzt . 2 jxrd i"r lirln dneqg dxcqdy d`xp .` :divwecpi`a a 1 = 0 ≤ 2 ( i a n ≤ 2 : n xear oekpy gipp ( ii a n +1 = 1 2 p a 2...
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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_5 - 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 5 lebxz...

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