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1、数学试卷2.3 数学归纳法一、选择题（每小题5 分，共 20 分）1一个关于自然数n的命题，如果验证当n1时命题成立，并在假设当nk(k1 且kN*)时命题成立的基础上，证明了当nk2 时命题成立，那么综合上述，对于()A一切正整数命题成立B一切正奇数命题成立C 一切正偶数命题成立D 以上都不对2在数列an 中，an112131412n112n，则ak 1()Aak12k1Bak12k212k4C ak12k2D ak12k112k2 3.设平面内有k条直线，其中任何两条不平行，任何三条不共点，设k条直线的交点个数为f(k)，则f(k1)与f(k)的关系是()Af(k1)f(k)k1 Bf(k
2、1)f(k)k1 C f(k1)f(k)kD f(k1)f(k)k2 4.用数学归纳法证明“当n为正奇数时，xnyn能被xy整除”，第二步归纳假设应写成()A假设n2k1(kN*)正确，再推n2k3正确B假设n2k1(kN*)正确，再推n2k1正确C 假设nk(kN*)正 确，再推nk1 正确D 假设nk(k1)正确，再推nk2 正确二、填空题(每小题 5 分，共 10 分)5用数学归纳法证明123n2n4n22时，当nk1 时左端在nk时的左端加上_6利用数学归纳法证明“(n 1)(n2)(nn)2n13(2n 1)，nN*”时，从“nk”变到“nk1”时，左边应增乘的因式是_三、解答题(共
3、 70 分)7.（15 分）对于nN*，用数学归纳法证明：1n2(n 1)3(n 2)(n1)2n 116n(n1)(n2)8.（20 分）已知正项数列an 和bn 中，a1a(0a 1)，b1 1a.当n2 时，anan 1bn，bnbn11a2n1.(1)证明：对任意nN*，有anbn1；(2)求数列 an 的通项公式9(20 分)数列 an 满足Sn2nan(nN*)数学试卷(1)计算a1，a2，a3，a4，并由此猜想通项公式an；(2)用数学归纳法证明(1)中的猜想10.（15 分）已知点Pn(an，bn)满足an1anbn1，bn 1bn1 4an2(nN*)且点P1的坐标为(1，1
4、)(1)求过点P1，P2的直线l的方程；(2)试用数学归纳法证明：对于nN*，点Pn都在(1)中的直线l上文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文
5、档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5
6、Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9
7、U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P
8、2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7
9、D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1
10、P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2数学试卷2.3 数学归纳法答题纸得分：一、选择题题号1 2 3 4 答案二、填空题5 6三、解答题7.8.文档编码:CY5X3F7D5Z8 HV10U1M1P
11、9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7
12、P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F
13、7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M
14、1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1
15、H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X
16、3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U
17、1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2数学试卷9.10.文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P
18、9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7
19、P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F
20、7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M
21、1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1
22、H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X
23、3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U
24、1M1P9U8 ZI1M4W1H7P2数学试卷2.3 数学归纳法答案一、选择题1.B 解析：本题证的是对n1,3,5,7，命题成立，即命题对一切正奇数成立2.D 解析：a1112，a21121314，an 112131412n112n，ak112131412k112k，所以，ak1ak12k112k 2.3.C解析：当nk1 时，任取其中1 条直线，记为l，则除l外的其他k条直线的交点的个数为f(k)，因为已 知任何两条直线不平行，所以直线l必与平面内其他k条直线都相交(有k个交点)；又因为已知任何三条直线不过同一点，所以上面的k个交点两两不相同，且与平面内其他的f(k)个交点也两两不相同，从
25、而平面内交点的个数是f(k)kf(k1)4.B 解析：首先要注意n为奇数，其次还要使n2k1 能取到 1.二、填空题5.(k21)(k22)(k 1)2解析：nk时左端为123k2，nk1 时左端为12 3k2(k21)(k22)(k1)2.6.2(2k1)解析：当nk(kN*)时，左式为(k1)(k2)(kk)；当nk1 时，左式为(k 11)(k12)(k1k1)(k1k)(k1k1)，则左边应增乘的式子是(2k1)(2k2)k12(2k1)三、计算题7.证明：设f(n)1n2(n1)3(n2)(n1)2n1.(1)当n1 时，左边 1，右边 1，等式成立；(2)设当nk时等式成立，即1k
26、2(k1)3(k2)(k1)2k116k(k1)(k2)，则当nk 1 时，f(k 1)1(k 1)2(k 1)1 3(k 1)2 (k 1)2 3(k 1)1 2(k1)1f(k)12 3k(k1)16k(k1)(k 2)12(k1)(k11)16(k1)(k2)(k3)由(1)(2)可知当n N*时等式都成立8解：(1)证明：用数学归纳法证明当n1 时，a1b1a(1 a)1，命题成立；假设nk(k1 且kN*)时命题成立，即akbk 1，则当nk1 时，ak1bk1akbk 1bk1(ak1)bk 1(ak1)bk1ak2bk1akbkbk1.当nk 1 时，命题也成立由、可知，anbn
27、1 对nN*恒成立(2)an1anbn 1anbn1an2an(1 an)1an2an1an，1an11anan1an1，文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M
28、4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:C
29、Y5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV
30、10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI
31、1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码
32、:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8
33、HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2数学试卷即1an11an 1.数列 1an 是公差为1 的等差数列，其首项为1a11a，1an1a(n1)1，从而ana1(n1)a.9.解：
34、(1)a11，a232，a374，a4158，由此猜想an2n12n1(nN*)(2)证明：当n1 时，a11，结论成立假设nk(k1，且kN*)时，结论成立，即ak2k12k1，那么nk 1(k1，且kN*)时，ak 1Sk1Sk2(k1)ak12kak2akak1.2ak 12ak，ak 12ak222k12k 122k112k，这表明nk1 时，结论成立an2n12n1(n N*)10.解：(1)由P1的坐标为(1，1)知a11，b1 1.b2b114a1213.a2a1b213.点P2的坐标为(13，13)直线l的方程为2xy1.(2)证 明：当n1 时，2a1b121(1)1 成立假
35、设nk(kN*，k1)时，2akbk1 成立，则当nk 1 时，2ak 1bk12akbk 1bk1bk14ak2(2ak1)bk1 2ak12ak12ak1，当nk 1 时，命题也成立由知，对nN*，都有 2anbn1，即点Pn在直线l上文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8
36、 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8
37、 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文
38、档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5
39、Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9
40、U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2文档编码:CY5X3F7D5Z8 HV10U1M1P9U8 ZI1M4W1H7P2