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1、高考数学难点突破训练数列与数学归纳法1.如图，曲线2(0)yx y上的点iP与 x 轴的正半轴上的点iQ及原点O构成一系列正三角形 OP1Q1，Q1P2Q2，,Qn-1PnQn,设正三角形1nnnQPQ的边长为na,n N(记0Q为O),0nnQS.（1）求1a的值;（2）求数列 na的通项公式na。2.设,nnab都是各项为正数的数列，对任意的正整数n，都有21,nnna ba成等差数列，2211,nnnbab成等比数列（1）试问nb是否成等差数列？为什么？（2）如果111,2ab，求数列1na的前n项和nS3.已知等差数列na中，2a 8，6S66.（）求数列na的通项公式；（）设nnan
2、b)1(2，nnbbbT21，求证：nT16.4.已知数列 na中531a，112nnaa（n 2，Nn），数列nb，满足11nnab（Nn）（1）求证数列 nb 是等差数列；（2）求数列 na 中的最大项与最小项，并说明理由；（3）记21bbSn,nb，求1)1(limnnSbnn5.已知数列 an 中，a10,且an+1=23na，()试求a1的值，使得数列an 是一个常数数列；()试求a1的取值范围,使得an+1an对任何自然数n都成立；()若a1=2，设bn=|an+1an|(n=1，2，3，,)，并以Sn表示数列 bn的前n项的和，求证：Sn0.Sn是它的前n 项和，又441S与66
3、1S的等比中项是117a，441S与661S的等差中项是6，求 an。26.na和nb分别是等比数列和等差数列，它们的前四项和分别为120 和 60，而第二项与第四项的和分别是90 和 34，令集合21aA，22a，23a，,，2na，1bB，2b，3b，,，nb求证：BA27.已知曲线 C：xy1，nC：nxy21（Nn）。从C上的点),(nnnyxQ作x轴的垂线，交nC于点nP，再从点nP作y轴的垂线，交C于点),(111nnnyxQ，设111,1nnnnnnyybxxax。（I）求21,QQ的坐标；（II）求数列na的通项公式；（III）记数列nnba的前n项和为nS，求证：31nS答案
4、：1.解：由条件可得11113,22Paa,代入2(0)yxy得21111312,0,423aaaa12nnSaaa11113(,)22nnnnPSaa；代入曲线2(0)yx y并整理文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编
5、码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R
6、3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5
7、 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文
8、档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S
9、7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3
10、N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2得2113142nnnSaa,于是当*2,nnN时,221113131()()4
11、242nnnnnnnaSSaaaa即11113()()()24nnnnnnaaaaaa*1120,(2,)3nnnnaaaannN又当2122231421,(4233nSaaa时舍去）；2123aa,故*12()3nnaanN所以数列 na 是首项为23、公差为23的等差数列,23nan。2.由题意，得212nnnbaa，（1）22211nnnabb（2）（1）因为0,0nnab，所以由式（2）得11nnnab b，从而当2n时，1nnnabb，代入式（1）得2112nnnnnbbbb b，即1122nnnbbbn，故nb是等差数列（2）由111,2ab及式（1），式（2），易得2233,2,
12、2ab因此nb的公差22d，从而12112nbbndn，得11122nann（3）又11a也适合式（3），得*12nn nanN，所以1211211nan nnn，从而111111221.2 1223111nnSnnnn3.解：（）11186,26 5666224nadadadand文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3
13、Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY
14、10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC
15、1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3
16、A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:
17、CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3
18、HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 Z
19、M3A3Q7K8T2（）2211(1)1)(24)12nnbnannnn（，121111111123344512nnTbbbnn，=1122n而1122n是递增数列，1111236nTT16.4.（1）1112111111nnnnnaaaab，而1111nnab，11111111nnnnnaaabb)(Nnnb是首项为251111ab，公差为1 的等差数列（2）依题意有nnba11，而5.31)1(25nnbn，5.311nan对于函数5.31xy，在x3.5 时，y 0，0y，在（3.5，）上为减函数故当n4 时，5.311nan取最大值3 而函数5.31xy在x3.5 时，y0，0)5.3
20、(12xy，在（，3.5）上也为减函数故当n3 时，取最小值，3a-1（3）2)5)(1(2)25225)(1(1nnnnSn，5.3nbn，nnnnnnnnSbn2)5)(1()5.3)(1(2lim)1(lim1文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N
21、5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2
22、文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2
23、S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z
24、3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8
25、T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3
26、F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T25.()欲使数列 an 是一个常数数列，则an+
27、1=23na=an 又依a10，可得an0 并解出：an=23，即a1=an=23()研究an+1an=23na231na=2323211nnnnaaaa(n2)注意到232321nnaa0 因此，可以得出：an+1an，anan 1，an 1an2，,，a2a1有相同的符号7要使an+1an对任意自然数都成立,只须a2a10 即可.由1123aa0，解得：0a123时，an+1an对任何自然数n都成立.因此当a1=2 时，an+1an0 Sn=b1+b2+,bn=|a2a1|+|a3a2|+,+|an+1an|=a1a2a2a3,anan+1=a1an+1=2an+1 又：an+2=231n
28、a23,故Sn0，t1，11tx原不等式等价于1ln11ttt令 f(t)=t-1-lnt，ttf11)(当),1(t时，有0)(tf，函数f(t)在),1(t递增f(t)f(1)即 t-1g(1)=0 tt11ln综上得xxxx11ln11（2）由（1）令 x=1,2,(n-1)并相加得112111ln23ln12ln13121nnnn文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY
29、10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC
30、1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3
31、A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:
32、CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3
33、HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 Z
34、M3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编
35、码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2即得11211ln13121nn7.(1)易求得nnpa（2）nnnnnnnnnpppSaCaCaCnf11)21(2121)(2211作差比较易得：)(21)1(nfppnf（3）当1n时，不等式组显然成立.当12)11(111)12()2()1(2nppppnfffn时，先证由（2）知)1()11()1()11()(11)1(2fppnfppnfppnfn)2()21()()21(1nppnfppnn1211212122)21(111211)21(121)21()21(21)(ninnnpppppppppppppp
36、ppif再证)()12()12()2()1(nfnnfffnnnppppppnffnff212)(11)21(12)12()1(2)12()1(而2212212)1(21)(1nnnnnppppppp)(211)21)(1(211)21(12)1(1)21(12)12()1(2)12()1(2nfppppppppppppnffnffnnnnnn同理：)(2)22()2(nfnff，)(2)32()3(nfnff，,，)(2)1()12(nffnf以上各式相加得：)()12(2)12()2()1(2nfnnfff文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文
37、档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S
38、7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3
39、N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T
40、2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F
41、2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8
42、Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K
43、8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2即)()12()(121nfnifni.8.（1）263510aaaa，又2621aa2637aa或2673aa若2673aa，则9nan，101a与0na矛盾；若2637aa，则1nan，显然0na，1nan（2）111lg2lg3,9bSb，当2n时，119lglg910nnnnbSS，欧19910nnb1n时，19nbb，199,10nnb
44、nN1910nnbb数列是以9 为首项，910为公比的等比数列。（3）199110nncn，设2kck是数列nc中的最大项，则由11kkkkcccc可得89k数列nc有最大项，最大项是78998110cc。9.（1）由,32)3(32)3(11mmasmmmasmnnnn得,3,2)3(1mmaamnn两式相减得,321mmaann文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A
45、3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3
46、H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q
47、7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY1
48、0A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1
49、I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A
50、3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:CY10A3F2S7R3 HC1I3H8Z3N5 ZM3A3Q7K8T2文档编码:C