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ex_sol(6)

# ex_sol(6) - Section 11.1 Sequences Instructor Ms Hoe...

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Unformatted text preview: Section 11.1: Sequences Instructor: Ms. Hoe Nguyen (nguyenaascsisuedu) 1 Sequence Notations A sequence is a list of numbers. The notation is: {an} 2 a1, a2, a3, Each number is called a term of the sequence. Example 1: [11.1.1a?’I—‘]The ﬁrst four terms of the sequence {(—2)""_} are . . l 1 u, D o cc Meta mi. (—27 z n_ i a l _.1. L" -| . '1”'2=4' a h: if“: '2) : '_ I 1 “ 0 é'xmzyﬁzul _ 5 a *‘.L -2 —2‘ ‘ C) 1,—2, —4,~8 ' ' a _'_z .-. — (-2 ‘* Example 2: n : ll. : (_ 2J3 _|‘_ l [11.1.1cPT] The n“ term of the sequence —1,%, mag, is — 2 2 l O (_1)n+1(%)n—1 avail (~l) (Llyi : , r z “73‘- n .1... n L n l I ° ‘» “iii—ﬂ (1+ 4: ("Wit 5 0 ("1) (2w) ‘ c s 1 o (—1)"+1(,~1;)"+‘r 7 n: 5: (-13 { gm. ' ' 5 125 A sequence can be deﬁned recursively, i.e., except the given ﬁrst term, each term of the 4 sequence is deﬁned by a formula involving the previous terms: 7 ‘ n _ 4. ' C 4 _ = L Example 3: " ' ‘1) “If 90] [11.1.1bPTlThe ﬁrst {menus oi'ihaiecﬂé’iié—Qéiéihegﬁéﬁby?“ = k" 3‘“"=”33—7m i 01:5 CLn= '7 ’7‘ 0’ None of these * ‘ o 3,——-‘~,6,-§ o aging o 3v 2 all 4; 2 Summation The ﬁnite and inﬁnite sums of a sequence {an}: 22:1 a]; = a1 + a2 + + a,h 2:1 ak = a1 + a2 + Note: k is called the index of summation. 1 Rules of the summation ' 22:10‘“: = 622:1 “k - 2::1c=cz:=11=m ‘ ELLA“): i bk) = 22:1 “k 5: 22:1 bk 0 22:1 ak = 2k"; ah + ELM“ ak where 1 < m < 11. Important Sums ' 22:1 k = w . 22:1 162 : ngn+11g2n+12 6 . 22:1 k3 = Example 4: > ‘ L t ' ﬂ 4 _I§m)‘ﬂ ~“[3;71.25.;PT1233L1(42—31%): 2 u — E 3k (A _ a. Q <— id‘hrm °'*i*%14 = L“ H — 3 k +(q-3.2)é‘2rxd‘hfmo "26”- _ 5 +0} -15. a)? 5rd 4who m8 __ __ T ’— +(‘;L; 5.“)ﬁaamﬁpw wk Jam = m, _ 3) a2 = _ m [11.1.2bPT]Se1ect the summation notation for 1 -— %+ g. .. . _ i 0 None of these Dc \ | u _ 0 22:0 :‘a H : ag= — —- (M’r -- 2.65"";fﬁza zus O C19: \/ M a a5: (43* z ( 1‘ 4.3x 5‘ 423 m 2% ,1]? )er m 2 clamug muck +Ll m LAST Jrerm; *Hum clad: Hu [@3er in /‘H/U.S\Jm, (wkckcm [3a k:0 or k:i). ...
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