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Lesson_13

# Lesson_13 - 'n1 ilxbhpi`e il`ivpxtic oeayg(104010 13 lebxz...

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Unformatted text preview: 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 13 lebxz xlw ilp :dkixr oxia xnr ,cwy inrp x"c ,ipinipa a`ei 'text :ddbd uixw di`n :dqtcd mixeh .ziteqpi` dxcq { a n } ∞ n =1 idz . ∞ X n =1 a n = a 1 + a 2 + a 3 + ... :xeh dpap :d`ad dxeva "miiwlg minekq" ly dycg dxcq dpap S 1 = a 1 S 2 = a 1 + a 2 . . . S n = a 1 + a 2 + ... + a n 1 dxcbd `xwp df leab .iteq leab yi { S n } miiwlgd minekqd zxcql m` qpkzn ∞ X n =1 a n xehdy mixne` :xehd mekq mb ∞ X n =1 a n = lim n →∞ S n .xcazn xehdy mixne` ,iteq `l e` miiw `l miiwlgd minekqd zxcq ly leabd m` :xehd zeqpkzdl igxkd i`pz .(xcazn xehd f` lim n →∞ a n 6 = 0 m`y raep o`kn) lim n →∞ a n = 0 f` ,qpkzn ∞ X n =1 a n m`-i` z` miaygn .dxcbda yeniy `id xehd ly zeqpkzdd zwical zeiqiqad zeiexyt`d zg` .z`fd dxcql leab miiw m`d miwceae miiwlgd minekqd zxcq ixa (itewqlh xeh) 1 libxz ∞ X n =1 ln 1 + 1 n + 2 :xehd zeqpkzd ewca :oexzt :zixabl`d zedfl al miyp ln 1 + 1 n + 2 = ln n + 3 n + 2 = ln( n + 3)- ln( n + 2) 1 :okl S n = n X k =1 (ln( k + 3)- ln( k + 2)) = (ln 4- ln 3) + (ln 5- ln 4) + ... + (ln( n + 3)- ln( n + 2)) = ln( n + 3)- ln 3 = ln n + 3 3 .xcazn xehd okl . lim n →∞ S n = lim n →∞ ln n + 3 3 = ∞ z`f lkae , lim n →∞ ln 1 + 1 n + 2 = 0 xeh zeqpkzdl igxkdd i`pzd z` miiwn xehdy al eniy .witqn eppi`e igxkd i`pz wx ok` `ed lim n →∞ a n = 0 i`pzdy mi`ex o`kn .xcazn , | q | < 1 m` wxe m` qpkzn ∑ ∞ n =0 q n ixhne`ib xehy xiyi aeyig ici-lr gked d`vxda . 1 1- q `ed (qpkzn `ed xy`k) enekqe 2 libxz ∞ X n =0 (- 1) n + 2 n 3 n :xehd zeqpkzd ewca 1 1- (- 1 3 ) = 3 4-l) mdipy miqpkzn ∞ X n =0 2 3 n-e ∞ X n =0- 1 3 n miixhne`ibd mixehd :oexzt . 3 3 4 enekqe ,qpkzn oezpd xehd okle (dn`zda 1 1- 2 3 = 3-le 3 libxz ∞ X n =0 (- 1) n + 4 n 3 n :xehd zeqpkzd ewca :oexzt (- 1) n + 4 n 3 n =- 1 3 n + 4 3 n ∞ X n =0 (- 1) n + 4 n 3 n mekqd xeh okl .xcazn ∞ X n =0 4 3 n xehd eli`e ,qpkzn ∞ X n =0- 1 3 n xehd .xcazn miiaeig mixeh 2 dxcbd .miilily-i` eixai` lky xeh `ed iaeig xeh mrt lk ik) dler zipehepen { S n } ely miiwlgd minekqd zxcq iaeig xeh ly dxcbdd i"tr m` qpkzn iaeig xeh ,xnelk .dneqg `id m` wxe m` zqpkzn okle (ilily-i` xai` mitiqen .dneqg ely miiwlgd minekqd zxcq m` wxe 2 4 libxz ∞ X n =1 | sin n | 2 n :xehd zeqpkzd ewca :oexzt iaeig xeh `ed xehd S n =...
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Lesson_13 - 'n1 ilxbhpi`e il`ivpxtic oeayg(104010 13 lebxz...

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