安徽高考文科数学 数列大题

安徽高考文科数学 数列大题 2013、19((本小题满分13分) 设数列a满足，,且对任意，函数 nN,*a,2aa，,8,,n124 , 满足 fxaaaxaxax()()cos-sin,,，，,,f'()0,nnnnn，，，，12122 1ab (?)求数列的通项公式;(?)若，求数列的前项和. nSba,，()2,,,,nnnnnan2 2012、(21)(本小题满分13分) x设函数fxx()sin,，的所有正的极小值点从小到大排成的数列为. {}xn2 (?)求数列;(?)设的前项和为，求。 {}x{}xSsinSnnnnn 2011、(21)(本小题满分13分) n，2n，2在数1和100之间插入Tn个实数，使得这个数构成递增的等比数列，将这个数的乘积记作，再令n n?1aT,lg. nn, {}a{}bSn(?)求数列的通项公式;(?)设baa,,tantan,求数列的前项和. nnnnnn，1 CCC2010、21.(本小题满分13分)设x,,…,,…是坐标平面上的一列圆，它们的圆心都在轴的正半轴上，12n 3rCCn且都与直线相切，对每一个正整数,圆都与圆相互外切，以yx,nnn，1 3y C{}r表示的半径，已知为递增数列. nn x {}r(?)证明:为等比数列; O n nr,1{}n(?)设，求数列的前项和. 1rn person in charge a fine of 50 Yuan. (8) no permit to work and the job in accordance with the provisions, on the job unit fined 300 yuan, the unit will charge a fine of 100 Yuan. 7.5.3 accident penalties (1) injuries fatalities directly punished 1~2 million. Direct responsibility for the accident and have the corresponding responsibility of leadership, such as concerning administrative sanctions, should be brought to the company or the relevant Department. (2) personal injury accident occurred, the direct punishment 0.5-10,000 yuan, responsible for the direct responsibility for the accident and the responsibility of leadership, such as concerning administrative sanctions should be dealt with by the personnel Department of the company. (3) personal injury accident occurs, the direct punishment 500-1000, who is directly responsible for the accident responsibility, give notice of criticism and 50-100 economic sanctions against them. (4) to conceal the accident, reported without undue delay or false, to inform the administrative leadership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500-1000 punishment. (5) significant near miss should be attempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding 2009、19((本小题满分12分) 已知数列{} 的前n项和，数列{}的前n项和 (?)求数列{}与{}的通项公式;(?)设，证明:当且仅当n?3时，, 2008、(21)(本小题满分12分) 设数列{a}满足a=a, a=ca+1-c, N*,其中a,c为实数，且c 0. n,,n1n+1n (?)求数列{a}的通项公式; n 11(?)设aebnan,,,,,N*，求数列,b,的前n项和S; ,,(1),nnnn22 (?)若0,a,1对任意N*成立，证明0,c1. n,,n 详解 2013、19(解:由a,2aa，,8fxaaaxaxax()()cos-sin,,，，,, ， 124nnnnn，，，，1212 ,,fxaaaaxax(),，,,--sin-cos ， faaaa'()--0,，,nnnnn，，，，1212nnnn，，，1212 ？a2aaa,， 所以，， 是等差数列. ,,nnnn，，12 d,1a,2a,4？,，,,，ann2-111()而 13n 111 (2) bann,，,，，,，，()()()22121nna，1nnn222 111-()n()221，，nn22 S,，n121-2 1()nn，，=31-n2 12,，，nn31-n2 x12,,2012、21、【解析】(I) ,，,,，,,,,,fxxfxxxkkZ()sin()cos02(),223 22,,, fxkxkkZ()022(),,,,,，,,,33 person in charge a fine of 50 Yuan. (8) no permit to work and the job in accordance with the provisions, on the job unit fined 300 yuan, the unit will charge a fine of 100 Yuan. 7.5.3 accident penalties (1) injuries fatalities directly punished 1~2 million. Direct responsibility for the accident and have the corresponding responsibility of leadership, such as concerning administrative sanctions, should be brought to the company or the relevant Department. (2) personal injury accident occurred, the direct punishment 0.5-10,000 yuan, responsible for the direct responsibility for the accident and the responsibility of leadership, such as concerning administrative sanctions should be dealt with by the personnel Department of the company. (3) personal injury accident occurs, the direct punishment 500-1000, who is directly responsible for the accident responsibility, give notice of criticism and 50-100 economic sanctions against them. (4) to conceal the accident, reported without undue delay or false, to inform the administrative leadership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500-1000 punishment. (5) significant near miss should be attempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding 24,, ,,,，,,，,fxkxkkZ()022(),,33 2,2, 得:当时，取极小值 得: xn,,2fx(),,,,xkkZ2(),n33 2, (II)由(I)得: xn,,2,n3 22nn,, ,，，，，,，，，，,,，,？？Sxxxxnnn2(123)(1),,nn12333 * 当时， sinsin(2)0Sk,,,,nkkN,,3()n 23,* 当时， S,,sinsinnkkN,,,31()n32 43,* 当时， S,,,sinsinnkkN,,,32()n32 * 得: 当时， sin0S,nkkN,,3()n 3* 当时， S,sinnkkN,,,31()n2 3* 当时， S,,sinnkkN,,,32()n2 2011、21(【解题指导】(1)解题的关键是注意等比数列的性质，如果两项的下标和等于另外两项的下标和，则这两项的乘积等于另外两项的乘积;(2)抓住两角差正切公式的变形，合理进行拆项求和. cc【解析】(1)设在数1和100之间插入n个实数构成数列，所以数列是以为首项的等比数列，c,1,,,,nn1 n，2n，222故Tccccc,,,,,,,？100，aTn,,，lg2(nN,); ，，nn，nnn12212，， (2)baann,,，，tantantan(2)tan(3)=1-tan(-n-2)?tan(n+3)-1 nnn，1 1= [tan(-n-2)+tan(n+3)]?tan(-n-2+n+3)-1= [tan(n+3)-tan(n+2) ]-1 tan1 1所以S=b+b+???+b=[(tan4-tan3)+(tan5-tan4)+???+(tan(n+3)-tan(n+2) ]-n n12ntan1 1=[tan(n+3)-tan3]-n tan1 【技巧点拨】本题命制新颖，主要考查等比数列、三角化简以及拆项相消法求数列的前n项和，同时注重对学生的转化划归能力的考查，较好的体现了考纲中“在知识网络交汇处 设计 领导形象设计圆作业设计ao工艺污水处理厂设计附属工程施工组织设计清扫机器人结构设计 试题 中考模拟试题doc幼小衔接 数学试题 下载云南高中历年会考数学试题下载N4真题下载党史题库下载 ”这一指导思想，也是函数与方程的数学思想方法的应用的最佳体现. 2010、21.(本小题满分13分)本题考查等比数列的基本知识，利用错位相减法求和等基本方法，考查抽象能力以及推理论证能力. person in charge a fine of 50 Yuan. (8) no permit to work and the job in accordance with the provisions, on the job unit fined 300 yuan, the unit will charge a fine of 100 Yuan. 7.5.3 accident penalties (1) injuries fatalities directly punished 1~2 million. Direct responsibility for the accident and have the corresponding responsibility of leadership, such as concerning administrative sanctions, should be brought to the company or the relevant Department. (2) personal injury accident occurred, the direct punishment 0.5-10,000 yuan, responsible for the direct responsibility for the accident and the responsibility of leadership, such as concerning administrative sanctions should be dealt with by the personnel Department of the company. (3) personal injury accident occurs, the direct punishment 500-1000, who is directly responsible for the accident responsibility, give notice of criticism and 50-100 economic sanctions against them. (4) to conceal the accident, reported without undue delay or false, to inform the administrative leadership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500-1000 punishment. (5) significant near miss should be attempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding3 133,解:(?)将直线的倾斜角记为，则有，. sin,,,,yx,tan233 r1n设的圆心为，则由题意知，得;同理. C(,0),,,,2r,,2rnnnnnn，，11,2n 从而，将代入，解得. ,,,，，,rrr2,,2rrr,3nnnnn，，，111nnnn，1 故为公比等比数列. {}rq,3n n1,nn,1(?)由于，，故，从而， r,1,,3nq,3r,31nrn 12n,,11n记，则有， ? Sn,，,，,,,，,1233S,，，,,,，nnrrr12n S,,,,121nnn,,，,，,,,，,,，,1323(1)33 ? nn3 ,n2S1333,,,,,121nn,,nnn,，，，,,,，,,?-?，得nn 13333n,,,,,，,3()33222 1,n9139(23)3,，,n1,n?. Sn,,，,,()3n4224 an (1) ,,1a,,ssn,, (2)ab和ab和nn,1,nnnn2009、19. 【思路】由可求出，这是数列中求通项的常用方法之一，在求出 cn后，进而得到，接下来用作差法来比较大小，这也是一常用方法。 as,,411【解析】(1)由于 22*assnnnnn,,,，,,，,,(22)[2(1)2(1)]4？,,annN4()n,2nnn,m1当时, ， bTTb,,,,,,(26)(2)？,2bbxn,nnnmm,,11nn,1又当时 11n,1？,b()nb,,n22？数列项与等比数列,其首项为1,公比为 ， 12(1)1n，,16(1)()n，,2Cn，(1)n，12？,,211221n,Cn221n,nCabn,,,,16()16()n,11n22(2)由(1)知 2C(1)n，n，1,,11得2Cn2n,3nnn,,,？,，21012n由即即 person in charge a fine of 50 Yuan. (8) no permit to work and the job in accordance with the provisions, on the job unit fined 300 yuan, the unit will charge a fine of 100 Yuan. 7.5.3 accident penalties (1) injuries fatalities directly punished 1~2 million. Direct responsibility for the accident and have the corresponding responsibility of leadership, such as concerning administrative sanctions, should be brought to the company or the relevant Department. (2) personal injury accident occurred, the direct punishment 0.5-10,000 yuan, responsible for the direct responsibility for the accident and the responsibility of leadership, such as concerning administrative sanctions should be dealt with by the personnel Department of the company. (3) personal injury accident occurs, the direct punishment 500-1000, who is directly responsible for the accident responsibility, give notice of criticism and 50-100 economic sanctions against them. (4) to conceal the accident, reported without undue delay or false, to inform the administrative leadership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500-1000 punishment. (5) significant near miss should be attempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding C(1)2n，n，1,1,12C,0CC,Cn,3n,3nnn，12nn又时成立,即由于恒成立.，因此,当且仅当时, 2008、解 (1) 方法一: a,1a,1 当时，是首项为，公比为的等比数列。 ?a,1?aca,,,1(1)c,,nnn，1 n,1n,1a,1 ，即 。当时，仍满足上式。 a,1?aac,,,1(1)aac,,，(1)1nnn n,1* 数列的通项公式为 。 ?aaac,,，(1)1()nN,,,nn 方法二 211nn,,n,2由题设得:当时， acacacaac,,,,,,,,,,1(1)(1)(1)(1)？nnn,,121 n,1 ?aac,,，(1)1n n,1*n,1?时，也满足上式。 数列a的通项公式为 。 aa,aac,,，(1)1()nN,,,n1n 1nn,1bnacn,,, (2) 由(1)得 (1)()n2 1112nSbbbn,，，，,，，，？？ 2()()nn12222 1111231n，Sn,，，，？ ()2()()n2222 1111121nn，?Sn,，，，,？()()() n22222 111111121nnnn,n?Snn,，，，，,,,,？?Sn,,，2(2)() 1()()()2[1()]()nn2222222 n,1(3) 由(1)知 aac,,，(1)1n n,1n,1若，则 0(1)11,,，,ac0(1)1,,,ac 1n,1*?,,,cnN0()?01,,,,aa 1,a1 n,1*c,0c,1c,0nN,由对任意成立，知。下面证，用反证法 n,1xc,1cn方法一:假设，由函数的函数图象知，当趋于无穷大时，趋于无穷大 fxc(), 1n,1*?c,1?01,,c?c,nN,不能对恒成立，导致矛盾。。 a,1 11n,1n,1c,1?c,?c,loglog方法二:假设，， cc,a,a11 1*nnN,,,1log()即 恒成立 (,) c,a1 *?c,1?01,,c?nN,?ac,为常数， (,)式对不能恒成立，导致矛盾， person in charge a fine of 50 Yuan. (8) no permit to work and the job in accordance with the provisions, on the job unit fined 300 yuan, the unit will charge a fine of 100 Yuan. 7.5.3 accident penalties (1) injuries fatalities directly punished 1~2 million. Direct responsibility for the accident and have the corresponding responsibility of leadership, such as concerning administrative sanctions, should be brought to the company or the relevant Department. (2) personal injury accident occurred, the direct punishment 0.5-10,000 yuan, responsible for the direct responsibility for the accident and the responsibility of leadership, such as concerning administrative sanctions should be dealt with by the personnel Department of the company. (3) personal injury accident occurs, the direct punishment 500-1000, who is directly responsible for the accident responsibility, give notice of criticism and 50-100 economic sanctions against them. (4) to conceal the accident, reported without undue delay or false, to inform the administrative leadership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500-1000 punishment. (5) significant near miss should be attempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding5