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1、数列知识点 1、等差数列的性质（2018 秋 6）记等差数列na的前n项和为nS，若30a，6714aa，则7S答案：14（2018 春 5）已知 na是等差数列，若2810aa，则357aaa_答案：1知识点 2：等差数列的判定（2017 秋 15）已知数列*2,Nncbnanxn，使得100200300,kkkxxx成等差数列的必要条件是（）A.0a B.0b C.0c D.02cba答案：A 知识点 3：等差数列的递推关系式（2013 年文 22）已知函数，无穷数列满足，（1）若，求；（2）若，且成等比数列，求的值；（3）是否存在，使得12,naaaLL成等差数列？若存在，求出所有这样的
2、1a；若不存在，说明理由解：（1）22a，30a，42a（2）21122aaa，321222aaa 当102a时，31122aaa，所以22112aa，得11a 当12a时，311224aaa，所以211142aaa，得122a（舍去）或122a综合 得11a或122a（3）假设这样的等差数列存在，那么212aa，3122aa由2132aaa得111222aaa（）以下分情况讨论：()2f xxna1()nnaf a*nN10a234,a a a10a123,a a a1a1a 当12a时，由（）得10a，与12a矛盾；当102a时，由（）得11a，从而1na1,2,nL，所以na是一个等差数
3、列；当10a时，则公差2111220daaaa，因此存在2m使得1212maam此时120mmmmdaaaa，矛盾综合 可知，当且仅当11a时，123,aaa L构成等差数列（2013 理 23）给定常数，定义函数数列123,aaaL满足，（1）若，求及；（2）求证：对任意，；（3）是否存在，使得12,naaaLL成等差数列？若存在，求出所有这样的；若不存在，说明理由解：（1）232,10aac（2）8,33+8,8,xcf xxcxc,4,4.xccxcxc当nac时，18nnaacc；当4ncac时，12382438nnnaaacccc；当4nac时，128248nnnaaacccc0c(
4、)24f xxcxc1()nnaf a*nN12ac2a3a*nN1nnaac1a1a文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:
5、CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I
6、6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9
7、HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z
8、2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5
9、ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8
10、Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3所以，对任意nN，1nnaac方法二：要证：24xcxcxc24xcxcxc当0
11、xc时，等式右边为0，不等式显然成立当0 xc时，等式化为242xcxc 显然（3）由（2），结合0c得1nnaa，即na为无穷递增数列又na为等差数列，所以存在正数M，当nM时，nac，从而，1()8nnnaf aac由于na为等差数列，因此其公差8dc 若14ac，则211()8afaac，又2118aadac，故1188acac，即18ac，从而20a当2n时，由于na为递增数列，故20naac，所以，1()8nnnaf aac，而218aac，故当18ac时，na为无穷等差数列，符合要求；若14cac，则211()338af aac，又2118aadac，所以，113388acac，得
12、1ac，舍去；若1ac，则由1naa得到1()8nnnaf aac，从而na为无穷等差数列，符合要求综上，1a的取值集合为,8ccU文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2
13、M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 Z
14、N10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z
15、5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3
16、文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:C
17、W9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6
18、M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3知识点 4：等比数列的性质（2015
19、 理 17）记方程 ：2110 xa x，方程 ：2220 xa x，方程 ：2340 xa x，其中123,aaa是正实数当123,aaa成等比数列时，下列选项中，能推出方程 无实根的是（）A方程 有实根，且 有实根B方程 有实根，且 无实根C方程 无实根，且 有实根D方程 无实根，且 无实根答案：B知识点 5：等比数列的判定（2011 理 18）设na是 各项 为 正数 的 无穷 数 列，iA是 边 长 为1,iiaa的 矩 形面 积（1,2,iL），则nA为等比数列的充要条件为（）A na是等比数列B 1321,naaaLL或242,naaaLL是等比数列C 1321,naaaLL和24
20、2,naaaLL均是等比数列D 1321,naaaLL和242,naaaLL均是等比数列，且公比相同答案：D 知识点 6：等差数列与等比数列综合（2016文22）对 于 无 穷 数 列na与 nb，记*|,nAx xa nN，*|,nBx xb nN，若同时满足条件：na，nb均单调递增；ABI且*ABNU，则称na与 nb是无穷互补数列（1）若21nan，42nbn，判断 na与nb是否为无穷互补数列，并说明理由；（2）若2nna且 na与nb是无穷互补数列，求数列nb的前 16 项的和；文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4
21、I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9
22、 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1
23、Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5
24、 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H
25、8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10
26、P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码
27、:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3（3）若na与 nb是无穷互补数列，na为等差数列，且1636a，求na与 nb的通项公式【解】（1）因为 4,4AB，所以4ABU，从而 na与nb不是无穷互补数列（2）因为416a，所以416 420b数列 nb的前16项的和为：2345120(1220)(2222)
28、20(22)1802L（3）设na的公差为,d dN，则1611536aad由136 151ad，得1d或2若1d，则121a，20nan，与“na与 nb是无穷互补数列”矛盾；若2d，则16a，24nan，,525,5nnnbnn综上，24nan，,525,5nnnbnn（2014 年理 23）已知数列满足1133nnnaaa，*nN，11a（1）若2342,9aax a，求x的取值范围；（2）设na是公比为q的等比数列，12nnSaaaL 若1133nnnSSS，*nN，求q的取值范围；（3）若12,kaaaL成等差数列，且121000kaaaL，求正整数k的最大值，以及k取最大值时相应数
29、列12,kaaaL的公差解：（1）由条件得263x且933xx，解得36x 所以x的取值范围是3,6x（2）由133nnaa，且110nnaaq，得0na，所以113nnSS又1133nnnaaa，所以133q当1q时，nSn，11nSn，由13nn得13nnSS成立当1q时，13nnSS即111311nnqqqq na文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M
30、3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH
31、4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M
32、9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN
33、10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5
34、U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文
35、档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW
36、9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3 若 13q，则(3)2nqq由nqq，nN，得(3)2qq，所以 12q 若113q，则(3)2nqq由nqq，nN，得(3)2qq，所以113q综上，q的取值范围为1,23（3）设12,kaaaL的公差为d由1133nnnaaa，且11a，得11(1)131(1)3ndndnd，1,2,1nkL即(21)2,(23)2,ndnd1,2,1nkL当1n时，223d；当2,1nkL时，由222123nn，得221dn，所以22213dk所以1
37、11210002221k kk kkadkk，即2200010000kk，得1999k所以k的最大值为1999，1999k时，12,kaaaL的公差为11999（2014 文 23）已知数列na满足1113,13nnnaaanNa（1）若1342,9aax a，求x的取值范围；（2）设na是等比数列，且11000ma，求正整数m的最小值，以及m取最小值时相应na的公比；（3）若12100,a aaL成等差数列，求数列12100,a aaL的公差的取值范围解：（1）由条件得263x且933xx，解得36x 所以x的取值范围是3,6x（2）设 na的公比为q由133nnaa，且110nnaaq，得
38、0na因为1133nnnaaa，所以133q从而111111()10003mmma qq，131000m，解得8m8m时，711,310003q所以，m的最小值为8，8m时，na的公比为741010文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10
39、H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U1
40、0P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编
41、码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z
42、4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W
43、9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X
44、1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A
45、5 ZN10H8Z5U10P3（3）设 数 列12100,aaaL的 公 差 为d 由133nnnaada，223nnada，1,2,99nL 当0d时，999821aaaaL，所以102da，即02d 当0d时，999821aaaaL，符合条件 当0d时，999821aaaaL，所以9999223ada，2(198)2(198)3ddd，又0d，所以20199d综上，12100,a aaL的公差的取值范围为2,2199知识点 7：数列的递推关系式与函数（2012 文 14）已知，各项均为正数的数列满足，若，则的值是答案：解：由，得，由，得，依次类推，得全体偶数项相等，所以（2017 春 21
46、）已知函数21log1xfxx（1）解方程1f x；（2）设1,1,1,xa证明：11,1axax，且11axffxfaxa；1()1f xxna11a2()nnaf a20102012aa2011aa26513311a2()nnaf a312a579112358,35813aaaa2()nnaf a211nnaa20102012aa2010201220101111aaa2010512a20082010201011aaa22010aa2011851313 513226aa文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4
47、X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9
48、A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN1
49、0H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U
50、10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档编码:CW9Z4I6M3W9 HH4X1Z2M9A5 ZN10H8Z5U10P3文档