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HW_sol

# HW_sol - Student’s Name MAC1140-24 Section 11.4 What...

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Unformatted text preview: Student’s Name: MAC1140-24 Section 11.4 What problems are the most difﬁcult for you? Question 1: (1 point) [11.4.1aPT]Find a; and as such that 1 + a? + a3 + - - n + an m i'orloallrtzgzzm4&3m7 ‘P: 4+al+05+,..+an: M524) :3 62:5,(13212 13;” +0; = 2(5:-\>_>4+qz= 5 I: a2=5,a3=9(n:2) r we) a ___ [3 None ofthese P3: 4+ 5.2 +05 ._. 5(3,5-\)=) 4+Ql+q4l Question 2: (1 point) (n: > _ [11.4.2aP’I‘]To prove by infuction that 7 + 4 + 1 + ~ -- + (10 — 3n) _ 15(1'2’71 - 3712) is true for all positive integers n, we assume 7 + 4 +1 + 17k —~ 3k2 is true for some ositive inte er k and ml. show that 7+4+1+ = H1709 +1) ‘30“ + “2] whereAis P“ :t + [t‘tl +..,+ 003m (inn—5711) I 7-3k , U 13__3k 11H: 1 + L;+\+.,,°+(\0T_5k)+ ﬂo—iUHD] E :w3kfi1ntk-H) ﬁx I ah, z =.oneo t ese :z[.+(k+'),5(k+b] E 11~3k Compm w‘xﬁx wthr m ma +9 SW} Question3:(1point):;) A : QH‘L‘ [0-5(k+l)= lO—ﬁk-B: [11.4.2bPT]To prove by induction that 7+ 5 + 3 + + (9 —- 2n.) = ' 8n—n2 istrue for all positive integers n, we assume 7+5+3+---+w, _[9 - 2k 2 8!: m- k" is true for some ositive integer k, and show that 7+5+3+~~+(9—2k)+(9—2(k+1)): whereAis '3 fk-k2+1 2 )E‘: 3L +5+5 +Mi +(9-Zn) = Xh—n" E: 8k+1)—(k +1P a , I “HUWWHF H, 3r +5 +5 +.... + (gfzk) + [9-2T(k+0]= ( =\+\ Col/M176“? wit/11 qul» W( "Idzjslwwi QK a %A:8(L+|)-(k+.)z 1 ' =8(k+x)_(lHD I: 8(k+l)—w(k+1)2+1 c 8(k+1)——(k2+1) Question 4: (1 point) ‘ [11.4.33PT]T0 prove by induction that n2 —- 712 m 4 is divisible by 219 true for all positive integers n, we assume 1:2 *- Tk -— 4 is divisible by 2 is true for some positive integar k, and we Show thath is divisible by gzherif ism 4 1 at V12- 2% - l} (s c‘wigigk E? Z ._ .__,. + a , . a (k + 1)?- “ 7(k + 1) m. 4 + 1PM ’ ("ma 4W“) -1; IS Clivié‘lzlxba 2 c “9+1ymnk+1y—4 QMHWA wwL NLa—wg Muiisgwf (’“+“’*7(k+”“4:~> A: aﬂoaicm- Li, C None of these Question 5: (1 point) [11.4.3bPT]To prove by inciuction that n2 - 77; -— 2 is divisible by 2 is true for all positive integers n, we assume is” - 7k -— 2 is ' ' ' is true for some positive integer k and we Show tha® divisible g3 Where A is ; ., ‘3 20””) PH: V3-4.“ -2 is cumin?) 1, C None of these I 2(k—3) Pk“: OGDL- -1 is cimsnbL La 2- r: 2(kw2) m p r: 202— 1,) (“A”)! @Hkn @S‘y \Z— 4k‘2 +2k-H-i LZ-jHK-Z +Zk-Q with wimi w: muci in slum») :3 A :— Zk'Q : 20(4)) ...
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