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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 =...
View Full Document

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.

Page1 / 9

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online