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2022年数列与数学归纳法专题2 .pdf

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1、数列与数学归纳法专题上海市久隆模范中学石英丽经典例题【例 1】已知数列na的前n项和为nS，且*,855NnanSnn.（1）证明：1na是等比数列；（2）求数列nS的通项公式，并求出使得nnSS1成立的最小正整数n.解：(1)当1n时，141a；当2n时，15511nnnnnaaSSa，所以16511nnaa.又01511a，所以数列1na是以 15 为首项，65为公比的等比数列.(2)由(1)知：165151nna，得1651nna从而*1,906575NnnSnn；由nnSS1得252651n，9.141252log65n，最小正整数15n.【例 2】等差数列na的前n项和为239,21

2、,31SaSn（1）求数列na的通项na与前n项和nS；（2）设()nnSbnnN，求证：数列nb中任意不同的三项都不可能成为等比数列解：（1）由已知得11213393 2aad，2d，故212(2)nnanSn n，（2）由（）得2nnSbnn假设数列nb中存在三项pqrbbb，（pqr，互不相等）成等比数列，则2qprbb b即2(2)(2)(2)qpr2()(2)20qprqprpqrNQ，2020qprqpr，22()02prprprpr，与pr矛盾所以数列nb中任意不同的三项都不可能成等比数列【例3】已知公差不为0 的等差数列na的首项1a为aRa,设数列

3、的前n 项和为4211,1,1,aaaSn且成等比数列.（1）求数列na的通项公式及nS；（2）记naaaaBSSSAnnn2221211111,1112，当2n时，试比较nA与nB的大小解：（1）设等差数列na的公差为d，由4122111aaa，得)3(1121daada.因为0d，所以ad所以21,1nanSnaann.（2）因为11121nnaSn，所以)111(211121naSSSAnn.因为aann1221，所以nnnaaaaaaBn211221121111111122221.当12,210nCCCnnnnnn时，即nn211111.所以，当nnnnBAaBAa时当时0;0.

4、【例 4】已知21a，点1,nnaa在函数xxxf22的图象上，其中=1，2，3，（1）证明数列na1lg是等比数列；（2）设nnaaaT11121，求nT及数列na的通项；（3）记211nnnaab，求数列nb的前项和Sn，并证明132nnTS=1.文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4

5、S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8

6、K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4

7、S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8

8、K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4

9、S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8

10、K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3解：（1）由已知212nnnaaa，211(1)nnaa12aQ11na，两边取对数得1lg(1)2lg(1

11、)nnaa，即1lg(1)2lg(1)nnaalg(1)na是公比为2 的等比数列.（2）由（）知11lg(1)2lg(1)nnaa1122lg3lg3nn1213nna（*）12(1)(1)nTaan(1+a)012222333n-12 321 223n-1+2=n2-13由（*）式得1231nna（3）nnnaaa2211(2)nnnaaa11111()22nnnaaa11122nnnaaa.又112nnnbaa1112()nnnbaa12nSbbn+b122311111112()nnaaaaaa+11112()naa.1221131,2,31nnnnaaaQ22131nnS.又213nn

12、T2131nnST.【例 5】已知数列na满足2,021aa，且对任意*,Nnm都有211212)(22nmaaanmnm.（1）求53,aa；（2）设)(*1212Nnaabnnn，证明：nb是等差数列；（3）设*11,0,Nnqqaacnnnn，求数列nc的前n项和nS.解：(1)由题意，6221,2123aaanm可得令，文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S

13、6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K

14、8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S

15、6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K

16、8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S

17、6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K

18、8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3再令20821,3135aaa

19、nm可得.(2)当*Nn时，由已知(以mn代替2)可得82121232nnnaaa.于是8)(1212112112nnnnaaaa，即6,81211aabbbnn.所以nb是以 6 为首项，8 为公差的等差数列.(3)由(1)(2)解答可知28,281212naanbnnn即.另由已知(令1m)可得211212naaann.那么nnnnaaaannnn21222812212121，于是12nnnqc.当1q时，12642nnnSn；当1q时，12102642nnnqqqqS.两边同乘以q，可得nnnqqqqqS2642321.上述两式相减得qnqqnnqqqnqqqqSqnnnnnnn1112

20、21122121112.所以21)1(112qnqqnSnnn.综上所述，1,11,111221qnnqqnqqnSnnn文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R

21、3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE

22、8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R

23、3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE

24、8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R

25、3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE

26、8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3数列与数学归纳法专题检测题一、填空题（每小题4 分，满分40 分）1.列na是首项为1，公比为23a的无穷等比数列，且na各项的和为a，则a的值是 .2.等比数列na的前 n 项和为nS，已知1S，22S，33S成等差数列，则na的公比为

27、 _.3.函数()2xf x,等差数列xa的公差为2.若246810()4f aaaaa,则212310log()()()()f af af af aL .4.知数列na、nb都是公差为1 的等差数列，其首项分别为1a、1b，且511ba，*11,Nba设nbnac（*Nn），则数列nc的前 10 项和等于.5.知数列na的首项10a，其前n项的和为nS，且112nnSSa，则limnnnaS .6.知等比数列na满足0,1,2,nanL，且25252(3)nnaan，则当1n时，2123221logloglognaaaL.7.差数列na的前 n 项和为nS，已知21

28、10mmmaaa，2138mS,则m.8.全体正整数排成一个三角形数阵：1 2 3 4 5 6 7 8 9 10 按照以上排列的规律，第n 行（n 3）从左向右的第3 个数为 .9.na是公比为q的等比数列，|1q，令1(1,2,)nnbanL，若数列nb有连续四项在集合53,23,19,37,82中，则6q=.10.知数列na满足：ma1（m为正整数），1,231,nnnnnaaaaa当为偶数时，当为奇数时。若6a 1，则m所有可能的取值为 _.二、解答题（本大题共有5 题，解答下列各题必须在规定区域内写出必要的步骤）11.设数列na满足11111011nnaaa且.文档编码:CA4G8C1

29、G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5

30、Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1

31、G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5

32、Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1

33、G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5

34、Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1

35、G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3（1）求na的通项公式；（2）设nabnn11，记nkknbS1,证明1nS.12.等比数列na中，321,aaa分别是下表第一、二、三行中的某一个数，且321,aaa中的任何两个数不在下表的同一列第一列第二列第三列第一行3 2 10 第二行6 4 14 第三行9 8 18（1）求数列na的通项公式；（2）若数列nb满足：nnnnaabln1，求数列nb的前 n 项和nS.13.设

36、d为非零实数，*11221,121NndnCdCndCdCnannnnnnnnn.（1）写出321,aaa并判断na是否为等比数列。若是，给出证明；若不是，说明理由；（2）设)(,*Nnndabnn，求数列nb的前 n 项和nS.14.设数列na的前 n 项和为nS，且方程02nnaxax有一根为,3,2,1,1 nSn（1）求21,aa；（2）na的通项公式15.已知有穷数列A：12,na aaL，(2n).若数列A中各项都是集合|11xx的元素，则称该数列为数列.对于数列A，定义如下操作过程T：从A中任取两项,ija a，将1ijijaaa a的值添在A的最后，然后删除,ija a,这样得

37、到一个1n项的新数列1A(约定:一个数也视作数列).若1A还是数列，可继续实施操作过程T，得到的新数列记作2A，L L,如此经过k次操作后得到的新数列记作kA.（1）设1 1:0,.2 3A请写出1A的所有可能的结果；（2）求证：对于一个n项的数列A操作 T 总可以进行1n次；（3）设5111 5 1 1 1 1 1:,.7654 6 2 3 4 5 6A，求9A的可能结果，并说明理由.文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X

38、8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:

39、CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X

40、8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:

41、CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X

42、8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:

43、CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X

44、8J9 ZX5Z8K8S1R3数列与数学归纳法专题检测题答案一、填空题1.2；2.13q；3.6；4.85；5.12；6.2n；7.10；8.262nn；9.9（提示81，54，36，24）；10.4 5 32；二、解答题11.设数列na满足11111011nnaaa且（1）求na的通项公式；（2）设nabnn11，记nkknbS1,证明1nS解：（1）由题设111111nnaa即na11是公差为 1 的等差数列。又1111a，故nan11所以nan11（2）由（I）得1111111nnnnnnnabnn，11111nbSnkkn12.等比数列na中，321,aaa分别是下表第一、二、三行中的

45、某一个数，且321,aaa中的任何两个数不在下表的同一列第一列第二列第三列第一行3 2 10 第二行6 4 14 第三行9 8 18（1）求数列na的通项公式；（2）若数列nb满足：nnnnaabln1，求数列nb的前 n 项和nS解：（1）当31a时，不合题意；当21a时，当且仅当18,632aa时，符合题意；当101a时，不合题意.因此18,6,2321aaa所以公式3q，故132nna文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S

46、8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编

47、码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S

48、8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编

49、码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S

50、8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编码:CA4G8C1G4S6 HE8X3S8X8J9 ZX5Z8K8S1R3文档编

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