从近几年高考试题看《数列》总复习

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12Ghanbn᦮ᦪḄ᦮ᦪnḄᦪ5.ᦑ⌱>fDo-2f2007ᐰI•ᳮ•15oF,ᦪᑡanḄbn⚗/Sn,}7SI,2s2,3S3ᡂF[ᦪᑡᑣanḄa,GhF,ᦪᑡanḄa,q,ᑣSIal,S2al1q,S3al1qq2.SI,2S2,3s3ᡂF[ᦪᑡSI3S34S2,EPal3a11qq24al1q,Z.q13.-3f2007ᐰII•ᳮ•16o}7ᦪᑡḄ_⚗an5n2,ᐸbn⚗/Sn,ᑣlimn->Snn2Ghᵫ_⚗a1«7ᦪᑡanF[ᦪᑡ✌⚗al3,a[d5,1
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Ḅὃ⚪ὃ^ஹF[ᦪᑡஹF,ᦪᑡḄ_⚗a1ஹbn⚗/a1ஹF[/F,ᦪᑡḄឋef᝞h“jṹ/”ឋe“ᱏn/”ឋeFoḄ⚪,,Ḇqr78Ḅὃ^01sᦪ⌱>⚪/?@⚪஺-1f2007xᓅ•ᳮ•8o}7~F[ᦪᑡan/bnḄbn⚗/ᑖAn/Bn,BAnBn7n45n3ᑣanbn᦮ᦪḄ᦮ᦪnḄᦪfo(A)2(B)3(C)4(D)5(ala2n1)2n1anbn2an2bnala2nlblb2n1A7n19122n17(blb2n1)(2nl)B2nInIn12Ghanbn᦮ᦪḄ᦮ᦪnḄᦪ5.ᦑ⌱>fDo-2f2007ᐰI•ᳮ•15oF,ᦪᑡanḄbn⚗/Sn,}7SI,2s2,3S3ᡂF[ᦪᑡᑣanḄa,

3GhF,ᦪᑡanḄa,q,ᑣSIal,S2al1q,S3al1qq2.,SI,2S2,3s3ᡂF[ᦪᑡ,SI3S34S2,KPal3al1qq24al1q,q13.-3f2007ᐰH•ᳮ•16o}7ᦪᑡḄ_⚗an5n2,ᐸbn⚗/Sn,ᑣlimnfSnn2Ghᵫ_⚗a1«7ᦪᑡanF[ᦪᑡ✌⚗al3,a[d5,1q2pr0,2qpr0,pr2pr,fpro0,pr.22³pr´µ.ᡠ·ᦪᑡbn¸¹3ḄW⚗&3«<ᡂF,ᦪᑡ.2ஹº»¼ᦪᑡᙠ
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4fCoᵬÈḄᐙ⌕ᩩËfDoᵬÎ3ÈḄᐙᑖᩩËÏ3ÈḄÍ⌕ᩩËGhÃanFT,ᦪᑡᑣanla2n2anla2n2,ᑣÐanpfpÑᦪnNo,Ó!ÔᨵpfpÑᦪnNoanlan·ᦪᑡan3F,ᦪᑡÇÕÃᦪᑡanF,ᦪᑡᑣᡠ·ᦪᑡanFT,ᦪᑡ஺ᦑ⌱>fBo஺anlanPÓ!Ôanla22P

52-8f20072Ö•ᳮ•20oÃᨵ×ᦪᑡal,a2...anfn᦮ᦪoÄÅalan,a2ᓽan1....analaiani1fi᦮ᦪB1ino,ÙÐÚᦪᑡ“ÛÐᦪᑡ”஺f1o}7ᦪᑡbn⚗ᦪ7ḄÛÐᦪᑡBbl,b2,b3,b4ᡂF[ᦪᑡbl2,b411,ᑏÝbnḄÞ!⚗.f2o}7cn⚗ᦪ2k1k1ḄÛÐᦪᑡBck,ck1...c2k1᪀ᡂ✌⚗50,a[4ḄF[ᦪᑡᦪᑡcnḄb2kᑣ*k1⚗/S2k1,3IâãS2k1äᑮᨬᜧâçᨬᜧâsèç(3)Ûéê»Ḅ᦮ᦪm1,ᑏÝᡠᨵ⚗ᦪ3ëì2mḄÛÐᦪᑡ1,2,22...2m1ᡂᦪᑡḄíî⚗Ç*m1500ãïᐸ!ᦪᑡḄb2008⚗/S2008.Gh(1)bnḄa[d,ðijb4bl3d23d11,Gd3,ᦪᑡbn2,,,5811,,,852.(2)S2k1clc2ck1ckck1c2k12(ckck1c2k1)ck,S2k14(k13)2413250,*k13ã,S2k1äᨬᜧâ.S2k1Ḅᨬᜧâ626.(3)ᡠᨵ«<Ḅ“ÛÐᦪᑡ”h2m2mIm22জ1,,22,,2,2,2,,2,,21Ç2m2mImIm22ঝ1,,22,,2,2,2,2,,2,,21Çm222m2m1ঞ2m1,2,,2,,,,2122,,2,2Çm222m2m1ট2m1,2,,2,,21,1,,22,,2,2.22007200821.Ûéজ*mN2008ãS20081222m2mIm22m2009222*1500mW2007ãS2008122

62m12m122m20092m2m122m20091.20081.Ûéঝ*m22008ãS20082*1500mW2007ãS20082m122m20081.mm2008Ûéঞ*m22008ãS200822.4*1500mW2007ãS20082m22009m3.Ûéট*m22008ãS20082m2m2008.*1500m<2007ãS20082m22008m2.apq-9f2007ø•ᳮ•14o}7ᦪᑡanÛ鸹p,qN*,ᨵapaq,Ãal19ᑣa36Ghúpq1,a2alalúpq2,a4a2a2úpq4,a8a4a4úpq8,al6a8a829,,,,329,4.4989169úpq16,a32al6a16úp32,q4,a36a32a43693ஹ⌴Âᦪᑡq¾ü⚪_Ñᵫ⌴Âa1êÝᦪᑡ³ᐸý78þÿ
ᙠὃᵨ⌴ஹᳮ᪀⌼஺Ḅ⌴ᜐᳮᨵ!1#$%᪀⌼&'ᦪᑡᩭ+$⚗

71᝞an+1=man+q(m,q7ᦪ)Ḅ⌴ᦪᑡ9ᓄ7(an+1+t)=m(an+t)(ᐸ=ᦪt=qm-1)ᩭ+?@(t+l)an+tan-lḄ⌴ᦪᑡ9ᓄ7an+l-2᝞an+l=+?@an=t(an-an-1)ᩭ3᝞an+l=an+tḄ⌴ᦪᑡ9ᓄ71ᩭ+?ᡈᵨEFG+?nan+ltn+1It9antn1JK9ᓄ74᝞anan1manpan10m,p7ᦪnNḄ⌴ᦪᑡPQRS◀U5anan19ᓄ7mp10,Wᑭᵨ1ḄG+?஺anlanSl(n1);5᝞Snfan,an1Ḅ⌴ᦪᑡᵨanᩭ?\஺SS(n2)n1n(2)$%EFஹE]ᡈE^ᩭ+$⚗1᝞an+l=an+f(n)Ḅ⌴ᦪᑡ9ᓄ7an+1-an=f(n)ᙠᵨ_]Gᩭ+ᐸ$⚗ᡈᑭᵨEFG+ᐸ$⚗@2᝞an+l=man+f(n)Ḅ⌴ᦪᑡᑭᵨEFG+ᐸ$⚗@3᝞an+l

8an=f(n)Ḅ⌴ᦪᑡᑭᵨE^GᡈEFG+ᐸ$⚗(3)$%`aᦪbcdGefᩭ+?$⚗g10(2007
i•ᳮ•14)ᙠᦪᑡan=kal1,an12an3(n1),ᑣmᦪᑡḄ$⚗an?n⌴ᐵpqᓄ7an132an3,anᡂstᦪᑡ✌⚗74,t72,an342nl2n1,an2n13.g11(2004ᐰx•ᳮ•22)yzᦪᑡ{an|=al=l,}a2k=a2k-a2k+l=a2k+3k,ᐸ=k=l,2,3,Ll+(-l)k,(1)+a3,a5@(2)+{an|Ḅ$⚗.?(1)a3=3,a5=13.(2)Qa2k+l=a2k+3k=a2k-l+(-1)k+3k,a2k+l-a2k-l=3k+(-l)k,a2k-l-a2k-3=3k-1+(-1)k-1,LL\a3-=al=3+(-1),a2kT1(a2k+b)+(a2kT-a2k-3)+L+(a3-lal)(3k+3k-kk-()+(-1)+L+3)+Sg-l+L+(-l)6\a2k+l-al=32(3k-l)+k(-1)-1/21,a2k+l=a2k=a2k-=3kl3k+12k+=12(-l)k-l,(-l)k-1+(-1)k3k2+12-l+(-l)k2+12(-l)-l.23,)g12(2007ᓅ•ᦻ•16)ᦪᑡan=al2an1ancn(cᦪn1,,,}al,a2,a3ᡂt71Ḅstᦪᑡ.

9!I#+cḄ;(II)+anḄ$⚗.?(I)al2,a22c,a323c,7al,a2,a3ᡂstᦪᑡᡠU(2c)22(23c),ᡠU(2c)22(23c),?c0ᡈc2.c0ala2a3,ᔠ⚪ᦑc2.(II)n22ᵫa2alc,a3a22c,anan1(n1)c,ᡠUanal[12(nl)]cn(nl)2c.3,).n1¡ᡂ¢ᡠ£al2,c2,ᦑan2n(n1)n2n2(n2,Uann2n2(n1,,2).*g13(2007¥¦•ᳮ•22)§¨᦮ᦪᦪᑡanª«a24,}¬®nN,ᨵ121an1anlnlan11n12lan.7(1)+al,a3@(3)+ᦪᑡanḄ$⚗an.??(1)¯ᩩ±2lan1111জn(n1)2an

10anan1142al24lai111,ᓽᨵn1ᵫ21222a2ala2al2?23al87.7al7¨᦮ᦪᦑal1.111,n2ᵫ2162a34a394?8a310,ᡠUa3

11(2)ᵫal1,a24,a39,`´ann2.µ☢ᵨᦪbcdGef.1n1,2ᵫ(1)zann2ᙳᡂ¢@2Ꮇ§nk(k22)ᡂ¢ᑣakᵫজ22k2¹nk1lak1111k(k1)222ak1kkak1k(kk1)k12k(kl)kk1222(k1)(k1)22

12k1ak1(k1)lk127k22(k21)(k1)2k(k1)(k2)20,ᡠU(k1)2k121,ᡠUlk10,1,l)^aklW(k1)22k10,1.£ak1N*,ᡠU(kᦑak1(k1)2,ᓽnk1ann2ᡂ¢.8ᵫ1,2z¬nN*,ann2.4ஹᦪ▣ᙠ¾¿ḄÀÀÁ⚪=Âᦪ▣ḄÁ⚪¡Ã?\ÄÅ⚪Ḅ᪶Ç⌕ÉÊᦪ▣Ḅ᤮ÌÍᑣ஺g14(2007Îᓭ•ᳮ•15)ÐᩰÒÓÔ=Ḅ᜻ᦪᣚᡂ1,Ꮤᦪᣚᡂ0,ᑮ᝞Ù1ᡠÚḄ0TÓÔᦪ⊤.ÜݵᦪÞ1ßᐰḄᦪà71ḄÞ1Þ2ßᐰḄᦪà71ḄÞ3”ÞnßᐰḄᦪà71ḄÞ@Þ61=1Ḅâᦪ.Þ11

131Þ2101Þ31111Þ410001Þ5110011,,,,，，，，，，，，，，，，，，，，，，，，，，，，1?᝞ÄãäÞ6Ḅᦪ71010101Þ7Ḅᦪ711111111Þ8Ḅᦪ7100000001ᵫÄ`´Þ2k1Ḅᦪà71（efᶍ#@ᵫU`´qzÞ637111111,,,,,,,,,,,,111111Þ6271010110101Þ6171100110011ᡠUÞ61ᐳᨵ32â1.g15（2005ç•ᳮ•12）ᵨnâSḄèᦪal,a2,,anqᑮn!âSḄ᣸ᑡêâ᣸ᑡ7JᑏᡂJân!Ḅᦪ▣஺¬Þiail,ai2,,ain,ìbiai12ai23ai3（l）nnain,i1,2,3,,n!.g᝞ᵨ1,2,3qᦪ▣᝞ÙᵫÄᦪ▣=êJᑡᔜᦪîïà12,ᡠUblb2b612212312241231312323121122ðñᙠᵨ1,2,3,4,5ᡂḄᦪ▣=blb2bl20=஺?ᙠᵨ1,2,3,4,5ᡂḄᦪ▣=êJᑡᔜᦪîïà360,blb2bl203602360336043605360108033Ù295ஹòᑡÄÅ⚪$àᢥôõÍᑣᙠö÷fx.y0øᡂJᑡòᯠúᩭûüýJᑡòḄþᙶ᪗ᡈᙶ᪗ᙠḄᐵ஺

1416(2007,ᦻ•22)ᦪf(x)=x2—4,#$%y=f(x)ᙠ'(xn,f(xn))ᜐḄᑗ%+x,Ḅ-'.(xn+1,0)(nN*),ᐸ3.45ᦪ.(I)ᵨxx⊤:xn+1;(II)

15xn22xn2(xn2)2xn2,gᳮxn12(xn2)2xn2ᦑxn12xn12(xn2xn2).2jklgxn12xn12n121gxn2xn2xl2x12Iᓽan12an.ᡠ_Iᦪᑡ｛an｝ᡂGHᦪᑡ.

16ᦑan2a12n1lg2n1lg3.ᓽlgxn2xn22n1lg3.10jkxn2xn232n1ᡠ_xn2(3322n11)12(3322n1n1(III)ᵫ(II)xn1)In1,Abnxn22n1432n1011132nlAbnIbn31132n32n113121113ln1mIdᯠT1bl23.ln1mIbn1121nIbn1()bn2Obi333/.Tnblb2bnblllnIbl()bl33lnbl[l()]113In33()3.3stITn3(nN*).

176ஹᦪᑡKTvwḄᦪᑡKT`OᨵXᑖzKT{ஹ|⚗}~{ஹ┯}{ஹNO{G஺vᵨḄKTNOX12n222n(n1)(2n1)6;12n333n(n1)422;012nnCnCnCnCn2.111<ᦪᑡanᡂGHᦪᑡIᦪᑡbnᡂGᦪᑡIᑣᦪᑡanbnḄSn⚗T[ᵨ┯}{KW஺1a2<ᦪᑡnᡂGᦪᑡIᑣᦪᑡḄSn⚗T[ᵨ|⚗}~{KW஺aann13+zᔠᦪᨵᐵḄKT⚪Iv⌮ᵨ⚗OᳮKW஺17(2007•ᳮ•17)#ᦪᑡanal3a232a3…3nlan(I)KᦪᑡanḄL⚗;(11)#bnnann3,aN*.KᦪᑡbnḄSn⚗TSn.2n1WX(I)al3a23a3…3ann3

18,জn132n2ln22mIal3a23a3…3an1.ঝজ-ঝ\3n1an13,an13nᙠজ3Icn1,\alan(II)bn13n13nannbnn3.23n

19Sn32333n3,ঞ234n13Sn32333…n3.টট-ঞ\2Snn3n1(333…3).ᓽ2Snn323nn13(13)13nSn(2n1)34n13418(2007▷•ᳮ•22)ᔜ⚗ᐰ.ḄᦪᑡDanEḄSk⚗T.Sk,¡12Sk12akakl(kN*),ᐸ3al1.(I)KᦪᑡDanEḄL⚗NO;

20(II)£¤¥¦Ḅ4᦮ᦪn(n22),ᦪᑡDbnEbkIbkknak12,n1)(k1,,,bl1,Kblb2bn.WX(I)lk1,ᵫalSI12ala2¨al1,\a22.12akak112aklak,\ak(ak1ak1)2ak.lk22mIᵫakSkSk1©.ak0,ᡠ_ak1ak12.jkªn11(m1)22mL*a2m2(m1)22m,mN*.ᦑakk(kN).(ID©.akk,ᡠ_bkIbknkak1nkk1ᡠ_bk

21bbk1(nk1)(nk2)(n1)k12bl1)1bkIbk2blk(k1)211bk(l)klCnk(k1,,2n).nᦑblb2b3bn7ஹᦪᑡsᔠ⚪1123nInCnCC(l)Cnnnn11Cnn112nn,CnCn(1)Cnnᦪᑡ+ᦪஹGOஹ`aG®Ḅsᔠ⚪v_ᦪᑡ®.¯%I°¨ᦪᑡḄᓫ²ឋஹᦪᑡḄᨬᜧ⚗ஹᦪᑡGOḄABG஺19(2007¶·•ᳮ•21)ᔜ⚗ᙳ.4ᦪḄᦪᑡanḄSn⚗TSnS11,¡6Sn(an1)(an2),nN.(I)KanḄL⚗NO;n

22(II)#ᦪᑡbnan(2b1)1,J?Tn.bnḄSn⚗TIKAX133Tn1log2(an3),nN.WX(I)WᵫalSI16W\al1ᡈal2,ᵫᎷ#alSI1,©»al2,(al1)(al2),16(an11)(an12)16(an1)(an2),¼ᵫan1Sn1Sn\(an1an)(an1an3)0,ᓽan1an30ᡈan1an,©an0,ᦑan1anᡂ½I¾¿.©»an1an3,jkanRN.3,✌⚗.2ḄGᦪᑡIᦑanḄL⚗.an3n1.(II)AXᵫan(2bn1)1[W\bnlog211log23n;a23n1jkTnblb2bnlog22536

233n133n363n2©»3Tn1log2(an3)log2.3n13n225c3n236f(n)3n13n2253,ᑣf(nl)f(n)3n23n3(3n3).23n53n2(3n5)(3n2)32©(3n3)3(3n5)(3n2)29n70,ᦑf(n1)f(n).ᱯÅᙢf(n)^f(l)27201,jk3Tn1log2(an3)log2f(n)0

24ᓽ3Tn1log2(an3).20(2007Ç•21)ᦪf(x)xx1,,R`af(x)0ḄÈÉ᪷(),f(x)Rf(x)ḄËᦪI#al1,an1anf(an)f(an)(n1,2,).2(1)KIḄÌ;(2)ABX£¤¥Ḅ4᦮ᦪn,Íᨵan;14ব?bnInanan(n1,2,),KᦪᑡbnḄSn⚗TSn.WXপf(x)x2x1,,R`af(x)=0ḄÈÉ᪷(),22;12n(2)f'(x)2x1,an1an

25aan12an1anan(2an1)12an1(2an1)55Vai1,•ᨵGO[a2-1Aa22_10gI᪵a3214(2an1)42an1

261222>JS-I(l¡Ñlal2mÒGÓ)III,,IIanan2an12(n=l,2,,,ᓽ(3)an1an2(an)(an)

272an1(an1)Ik11>an1(an)2an1,gᳮan12(an)2an1,bn13+x/53-/3+/2bn,¼blIn11In21n23+/Sn

282(2l)lnn1,,23,….21(2007ᐰÔI•ᳮ•22)ᦪᑡan3al2,an11)(an2),(I)KanḄL⚗NO;23,…I(II)<ᦪᑡbn3bl2,bn13bn4,n1,,2bn323,….bnWa4n3,n1,,WXÖI×ᵫ⚪#Xan141)(an2)1)(an1)(2

291)(anan11)(an.15ᡠ_IᦪᑡanR✌⚗.2an1)n,ᓽanḄL⚗NO.an(IDᵨᦪØÙÚ{AB.1ḄGHᦪÛu,n23,….1)1,n1,,

30(i)ln12,blal2biWal,ÜÝᡂ½.ÖÞ×Ꮇ#l஺kbkWßa4k3,àᓽ0bklnk1m,bk12+3á¼12bk3a4k33bk42bk3

31(32â)(46(3bk(42bk32bk30,3ᡠ_bk1(3b2k)2bk32)(322bk)

32ß2)WD4(a4k3a4k1àãRäIlnk1mIÜÝᡂ½.23,….bnWa4n3,n1,,x22(2007åᓭ•ᳮ•22)An(an,bn)(nN*)R$%y6tḄ',ala,3,,4„.SnRᦪᑡDanEḄSn⚗TI¡Sn3nanSn1,an0,n2,222bn2(I)ABXᦪᑡ(n<2)Rvᦪᦪᑡ;bn(IDèaḄÒÌéᔠM,ëaMmIᦪᑡDanERᓫ²⌴íᦪᑡ;(III)ABXlaMmஹîAnAn1(nN*)Ḅï᳛ñnᓫ²⌴í.222WX(I)ln22mIᵫ\SnSn13nan.16©.anSnSn10,ᡠ_SnSn13n2.,,,,জòRSn1Sn3(n1)2.,,,,ঝᵫঝóজ\an1an6n3.„„ঞòRan2an16n9.টᵫটóঞ\an2an6,„„ঠᡠ_

33bn2bnean2aneean2ane,ᓽᦪᑡ6bn2(n22)Rvᦪᦪᑡ.bn(II)ᵫজᨵS2SI12,ᡠ_a2122a.ᵫঞᨵa3a215,a4a321,ᡠ_a332a,a4182a.kঠ⊤BXᦪᑡDa2kETDa2k1EᑖÅR_a2,a3.✌⚗I6.NḄGᦪᑡIᡠ_a2ka26(k1),a2k1a36(k1),a2k2a46(k1)(kN*),ᦪᑡDanERᓫ²⌴íᦪᑡala2¡a2ka2k1a2k2£¤¥ḄkN*ᡂ½.ala2¡a26(k1)a36(k1)a46(k1)ala2a3a4a122a32a182aᓽᡠKaḄÒÌéᔠRMa94a15.4ean194a154

34(Ill)îAnAn1Ḅï᳛.knxbn1bnan1anxOeanan1an¤ÒxO,#ᦪf(x)xxOxOᑣf(x)e(xxO)(eeO)(xxO)2XXxxxxxx?g(x)e(xxO)(ee),ᑣg(x)e(xxO)eee(xxO))t.íᦪIlxxOmIg(x)0,g(x)ᙠ(xO,17lxxOmIg(x)0,8ö)ᙠ(IxO)t.ᦪ,

35ᡠ_XxOmIgÖx×gÖxO×0,jkf'Öx×0,ᡠ_£6×ᙠÖ,xO×TÖxO,×tÍRíᦪ.ᵫÖII×IaMmIᦪᑡDanEᓫ²⌴íIÒxOan,©.anan1an2,ᡠ_knean1eanan1anean1ean2eanan2aneanÒxOan2,©.anan1an2,ᡠ_kn1ean2e

36an2an1an2anan2ᡠ_knkn1,ᓽîAnAn1(nN*)Ḅï᳛ñnᓫ²⌴í.Lùᙢᙬ:üýþÿ
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