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hw7 - HOMENORK “1 501.111” 0N3 Prod L“ ‘P(Dq L61...

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Unformatted text preview: HOMENORK “1 501.111” 0N3 Prod L“; ‘P% \(Dq L61- POI) bc 'Vhe Skakmerrk 15123“ .+ 117’?“ (n+1) l4— .5 56mm 13 = PONY/4,901 '15 1.1112. Suppose 1111013: 12041 ’15. 112112 .Then 513+23+ . .+ 1<3= 1<=L+<++1‘,/+ Hence, 5 5 .5 5, _ 51‘ + 23+ +1<3 + (14-1113 = 1420411174: +. (14151)3 3 5 40011741114114.1041 5 . = (141511 (141-2.) 1.4:. 5 111519. proves M Pam) +5 11-51235 There§ore P505511 is true for a\\ posmue 55 5 51ntegers r1. Prob\em ”2.1a ‘ * La P1111 be ﬁne M11131} , 52: +1134 (91+ .~ (2n) = (2n)L2n+1) 1.2m 7.1/1.1 111m PG) '15. *rue,s1nce C-2)L2+11(2+7—)/(9 New. Suppose M P504.) 1S We. The“ ‘9. +4‘.+5. ..+(2141‘ = (2141(214+11L214+521lb and Ne aF’r. . 5. 5 22 .42 5(2141‘ + (214+ 21‘ = ((2141cz14111(214+21/191 ‘1 (214+21" 5 5 ((22+211b)(4\4"+214+12\< +512) 5 =Cz14-1215C214-13)(2\4+4)/(v. . . 5Th+$proves M 1764-1111 is me.1—1an4e, b151nduc‘don 1s ~11~v+c for 411 5pos‘1ﬁve 111163ch +1. 1 5 WProbbm *3 9% 119°) W Le1 Pan) be he smﬁemenk _\+o\-1-Q75‘+... +0.“.5:55..L"”—1)/Ca+-1) PC11 +5 true. because..- 115.02: La ~11/(a~11.1.1-‘ 904.1. .19 1ru€.,.:\1103+_. 451$, 1? _l+a+o?' + “a; = L. -11/(a1~11 +hen _. 51+m+ 41“ + “on 14““ — (( o.“*.‘—11/(54L~111+ 03‘“ 5: of“ ~~\, 41- 03“ (an-11 . . 5 5. 5.5.5W_.Q~ “5551 - 5-503" -1 , Q71. 5 5 . . (b) \"wﬂ = 0+,Hn , _ ‘(O Hn '= “(043/27 gpmuem *ZLo—Pg m ' Appha 'Hne binomial More!“ mm cu.- \ , b: -\. ...
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