2004年安徽省高中数学竞赛初赛

=IBA+IAB=ABC2+BAC2.,IBD=BID]ID=BD.BOIA1,A1O,IA1=IB,OIA1=OIB=30.,BIA1=OIB+OIA1=60.,A1BI,A1B=A1I.ID=BD,A1DBI,BA1I.BAD=BA1D=12BA1I=30.,BAC=2BAD=60.(1)x2-x-1=0,,+=1,=-1.n+2-n+2=(+)(n+1-n+1)-(n-n)=(n+1-n+1)+(n-n).,n+2-n+2-=n+1-n+1-+n-n-,an+2=an+1+an.(2){an},an=n-n-(n=1,2,),a1=--=1,a2=2-2-=+=1.n,an+2=an+1+an,,{an}.,.,(an+2,an+1)=d1.n,an+2=an+1+an,d=(an+2,an+1)=(an+1,an)=(an,an-1)==(a4,a3)=(a3,a2)=(1,1)=1,d1.,{an}.()2004()(6,36)1.ab0.,().(A)1a1b(B)1a-b1a(C)|a||b|(D)a2b22.y=log12(2x-x2)().(A)(0,2)(B)[1,+)(C)[1,2)(D)(0,1]3.SA{1,2,,26},S25.S().(A)10(B)11(C)12(D)134.0,2.sin+cos1().(A)sin+cos1(B)sin+cos1(C)sin+cos=1(D)15.1,ABCD-ABCDAABBMABBC.,M().(A)(B)(C)(D)6.A(a,b),B(c,d),63©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(a-c)2+(b-d)20,Pn(nN+)AP1=12AB,BP2=12BP1,PnPn+2=12PnPn+1.limnAPn().(A)c-a3,d-b3(B)c-a2,d-b2(C)2(c-a)3,2(d-b)3(D)3(c-a)4,3(d-b)4(9,54)7.abc,a2+b2+c2=ab+bc+ca,.8.35,3,k3k+132k-15,3,5,3,5,5,3,5,5,5,5,3,.2004S2004=.9.l:y=x+b0b12y2=2xAB,O.AOB,l.10.1,.60,.11.,400,500.AB.A48,46;B58,5.AB.12.f(x)=12x+a,x0,f(x-1),x0,f(x)=x.a.(20,60)13.f(x)(-1,1),f12=-1,xy(-1,1),f(x)+f(y)=fx+y1+xy.(1){xn}x1=12,xn+1=2xn1+x2n.an=f(xn),{an};(2)bn=n2+3n+1,1+f1b1+f1b2++f1b2002+f12004.214.2,MNABCDABCD,BNMCP,ANMDQ.:SMQNP=SBCP+SADQ.15.,,.,.1,6?1.B.ab0,aa-b0.1a-b1a.2.D..3.C.S={1,2,5,6,7,11,12,16,17,21,22,26}.4.A.0sin2,,sin+cossin2+cos=1+cos(1-cos)1.5.A.BCAABB,MBBC.,MBAB.,M.6.C.PnAB21.7..7320055©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(2k-1+1).2004k,kk+1+2++2k-12004.k=11.S2004=52004-211=9998.9.y=x+13.|AB|=221-2b,OABd=b2,SOAB=b1-2b.b=13,39.10.19.23.11.4720.ABxy.x0,y0,4x+5y400,6x+5y500.P=48x+58y.12.(-2,+).13.(1)y=x,2f(x)=f2x1+x2.xn+1=2xn1+x2n,,f(xn+1)=2f(xn).an+1=2an.a1=f12=-1,{an}-12.,an=-2n-1.(2)x=y=0,f(0)+f(0)=f(0).f(0)=0.y=-x,f(x)+f(-x)=f(0)=0.f(-x)=-f(x).f1bn=f1n2+3n+1=f1(n+1)(n+2)-1=f1(n+1)(n+2)1-1(n+1)(n+2)=f1n+1-1n+21-1(n+1)(n+2)=f1n+1+f-1n+2=f1n+1-f1n+2,1+f1b1+f1b2++f1b2002+f12004=1+f12-f13+f13-f14++f12003-f12004+f12004=1+f12=0.14.SADQ=12SADB-SAQM,SBCP=12SACB-SMBP,SADQ+SBCP=12SADB+12SACB-SAQM-SMBP.SMQNP=SANB-SAQM-SMBP,SANB=12(SADB+SACB).AB,hh1h2.NCDh=12(h1+h2).12AB,12ABh=1212ABh1+12ABh2.,SANB=12(SADB+SACB).,SMQNP=SADQ+SBCP.15.,12+123+125+=121-122=23.1-23=13.{k}={k-1k}{k-1k}.Pkk,P1=23,Pk=13Pk-1+23(1-Pk-1)=23-13Pk-1]Pk-12=-13Pk-1-12]Pk=12+(-1)k-13k-1P1-12=12+(-1)k-123k.,P6=364729.6364729.()83©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.