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当前位置：首页 > 教育专区 > 高考资料 > 2022年数学练习题考试题高考题教案第2讲递推数列、数列求和、数学归纳法 .pdf

2022年数学练习题考试题高考题教案第2讲递推数列、数列求和、数学归纳法 .pdf

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1、专题三数列第 2 讲数列求和、递推数列、数学归纳法教学目标：1.能利用等差、等比数列前n 项和公式及其性质求一些特殊数列的和。2.能利用 Sn与 an的关系11(1)(2)nnnS naSSn解题。3.了解递推关系是给出数列的一种方法，能通过对递推式的变形将递推数列问题转化为等差数列或等比数列问题来解决。4.理解“归纳猜想数学归纳法证明”的解题思想。教学重点：能利用等差、等比数列前n 项和公式及其性质求一些特殊数列的和。教学难点：通过对递推式的变形将递推数列问题转化为等差数列或等比数列问题。热身练习：1.设1)1()(3xxf，利用课本中推导等差数列的前n项和的公式的方法，可求得)6()5()

2、0()4(ffff的值为：2.若满足21a，)2(11nnnaann，则4a=（）（A）34（B）1（C）54（D）323.若na的前n项和21nnS,则2222123naaaa例题 1：设数列0,1,)1(,其中且项和为的前nnnnaSSna（1）证明：数列na是等比数列；（2）设数列na的公比()qf，数列nb满足1b12，bn=f(bn-1)(nN*,n 2),求数列nb的通项公式；（3）记1，1(1)nnnCab，求数列nC的前 n 项和n变式 1：设na是等差数列，nb是各项都为正数的等比数列，且111ab，3521ab，5313ab（）求na，nb的通项公式；（）求数列nnab的前

3、 n 项和nS例题 2：已知数列na的前 n 项和为 Sn，且11,nnS a成等差数列，*1,1Nna函数3()logf xx（I）求数列na的通项公式；（II）设数列nb满足1(3)()2nnbnf a，记数列nb的前 n 项和为 Tn，试比较52512312nnT 与的大小变式 2：已知二次函数()yf x的图象经过坐标原点，其导函数为()62fxx，数列na的前n项和为nS，点(,)()Nnn Sn均在函数()yf x的图象上(1)求数列na的通项公式；(2)设13nnnba a，nT是数列nb的前n项和，求使得20nmT对所有Nn都成立的最小正整数m.例题 3：设pq，为实数，是方程

4、20 xpxq的两个实根，数列nx满足1xp，22xpq，12nnnxpxqx（34n，）（1）求数列nx的通项公式；（2）若1p，14q，求nx的前n项和nS变式 3：在数列na中，1112(2)2()nnnnaaanN，其中0（）求数列na的通项公式；文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码

5、:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G1

6、0B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J

7、6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I

8、10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9

9、K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4

10、D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6

11、A7文档编码:CO6G10B6C8J6 HN2I10H8D9K9 ZL4D7B9R6A7（）求数列na的前n项和nS；例题 4：已知各项全不为零的数列 ak的前 k 项和为 Sk，且 Sk11(2kka akN*），其中 a1=1（）求数列 ak的通项公式；（）对任意给定的正整数n（n2），数列 bk 满足11kkkbknba（k=1，2，n-1），b1=1 求b1+b2+bn.变式 4：已知()nnnAab，（nN*）是曲线xye上的点，1aa，nS是数列na的前n项和，且满足22213nnnSn aS，0na，2 34n，（I）证明：数列2nnbb（2n）是常数数列；（II）确定a的取值集

12、合M，使aM时，数列na是单调递增数列.归纳：1.利用 Sn与 an的关系11(1)(2)nnnS naSSn解题要注意分类讨论。2.求递推数列的通项的分析方法有：（1）构造新数列（等差或等比）；（2）累加法、累乘法、迭代法等；（3）归纳猜想数学归纳法证明。3.数列求和常见的四种方法：倒序相加、裂项相消、错位相减、分解求和。作业：1.若数列na满足：nnaa111且21a，则2009a（）（A）1（B）1（C）2（D）212.已知数列na满足11a，1321)1(32nnanaaaa，则2n时，数列na的通项na（）（A）!2n（B）(1)!2n（C）!n（D）(1)!n文档编码:CZ3O4A

13、9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9

14、HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V

15、3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7

16、 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2

17、R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M

18、5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:

19、CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M53.已知两个等差数列na和nb的前n项和分别为An和nB，且74 53nnAnBn，则使得nnab为整数的正整数n的个数是（）A2 B3 C4 D5 4.2232121234(1)nn的值为

20、5.由111,31nnnaaaa给出数列na的第 34 项是6.已知正项数列na的前 n 项和为nS，且1212444222nnnSSSSaaa，则na7.数列na中，12a，1nnaacn（c是常数，12 3n，），且123aaa，成公比不为1 的等比数列（I）求c的值；（II）求na的通项公式8.OBC的各个顶点分别为(0,0),(1,0),(0,2)，设1P为线段BC的中点，2P为线段 OC 的中点，3P为线段1OP的中点对每一个正整数3,nn P为线段1nnP P的中点令nP的坐标为(,)nnxy，1212nnnnayyy（1）求321,aaa及,()Nnan；（2）证明：41,()4

21、Nnnyyn（3）记444,()Nnnnbyyn，证明：nb是等比数列教师版专题三数列文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:

22、CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A

23、9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9

24、HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V

25、3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7

26、 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2

27、R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5第 2 讲数列求和、递推数列、数学归纳法教学目标：1.能利用等差、等比数列前n 项

28、和公式及其性质求一些特殊数列的和。2.能利用 Sn与 an的关系11(1)(2)nnnS naSSn解题。3.了解递推关系是给出数列的一种方法，能通过对递推式的变形将递推数列问题转化为等差数列或等比数列问题来解决。教学重点：能利用等差、等比数列前n 项和公式及其性质求一些特殊数列的和。教学难点：通过对递推式的变形将递推数列问题转化为等差数列或等比数列问题。热身练习：1.设1)1()(3xxf，利用课本中推导等差数列的前n项和的公式的方法，可求得)6()5()0()4(ffff的值为：11 解：课本中推导等差数列的前n项和的公式的方法即为“倒序相加法”令Sfffff)6()5()0()3()4(

29、则也有Sfffff)4()3()2()5()6(由21)1(1)1()2()(33xxxfxf可得：2)5()3()6()4(ffff，于是由两式相加得2112S，所以11S2.若满足21a，)2(11nnnaann，则4a=（C）（A）34（B）1（C）54（D）323.若na的前n项和21nnS,则2222123naaaa1(41)3n例题 1：设数列0,1,)1(,其中且项和为的前nnnnaSSna（1）证明：数列na是等比数列；（2）设数列na的公比()qf，数列nb满足1b12，bn=f(bn-1)(nN*,n 2),求数列nb的通项公式；（3）记1，1(1)nnnCab，求数列nC

30、的前 n 项和n解：(1)由11(1)(1)(2)nnnnSaSan相减得：11,(2),1nnnnnaaaana数列na是等比数列(2)1111(),111nnnnnbfbbbb文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5

31、文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:C

32、Z3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9

33、Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 H

34、W5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3

35、X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7

36、ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R

37、9T10M51nb是首项为112b，公差为 1 的等差数列，12(1)1nnnb11nbn(3)1时，11111,(),(1)()22nnnnnnaCanb2111112()3()()222nnTn2311111()2()3()()22222nnTn得：2311111111()()()()()222222nnnTn231111111111()()()()()2(1()()22222222nnnnnTnn所以：114(1()2()22nnnTn变式 1：设na是等差数列，nb是各项都为正数的等比数列，且111ab，3521ab，5313ab（）求na，nb的通项公式；（）求数列nnab的前 n

38、项和nS解：（）设na的公差为d，nb的公比为q，则依题意有0q且4212211413dqdq，解得2d，2q所以1(1)21nandn，112nnnbq（）1212nnnanb122135232112222nnnnnS，3252321223222nnnnnS，得22122221222222nnnnS，文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9

39、V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K

40、7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M

41、2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10

42、M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码

43、:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4

44、A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9

45、 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M52211112122(1)2222nnn1111212221212nnn12362nn例题 2：已知数列na的前 n 项和为 Sn，且11,nnS a成等差数列，*1,1Nna函数3()logf xx（I）求数列na的通项公式；（II）设数列nb满足1(3)()2nnbnf a，记数列nb的前 n 项和为 Tn，试比较52512312nnT 与的大小解：（I）11,nnSa成等差数列，121nnSa当2n时，121nnSa得：112()nnnnSSaa，13n

46、naa，13.nnaa当 n=1 时，由得112221Saa，又11,a2213,3,aaa2213,3,aaana是以 3 为公比的等比数列，13.nna（II）133()log,()log 31nnf xxf an，133()loglog 31nnnf aan，11111()(3)()2(1)(3)213nnbnf annnn，1111111111111()2 24354657213nTnnnn1 1111()2 2323nn525,122(2)(3)nnn比较52512312nnT 与的大小，只需比较2(2)(3)nn与 312 的大小即可文档编码:CZ3O4A9Z4F9 HW5O9V3

47、X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7

48、ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R

49、9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5

50、文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:CZ3O4A9Z4F9 HW5O9V3X10K7 ZR5M2R9T10M5文档编码:C

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关键词：: 2022年数学练习题考试题高考题教案第2讲递推数列、数列求和、数学归纳法 2022 数学练习题考试题考题教案讲递推数列求和归纳法

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