新課標高考數(shù)列《數(shù)列求和》大題專題含答案

1、2021高考數(shù)學專題復習：數(shù)列2021.4.6數(shù)列求和1.公式求和.222211.123n-n(n1)(2n1)62132333n3n(n1)22.-13.數(shù)列an中,a12,q一3(I)求an,Sn(n)bnlog3a110g3a210g3a3log3an,求bn4.數(shù)列an的前n項和Sn和通項an滿足Sn(an1)(q是常數(shù)且q0,q1q1(i)求數(shù)列an的通項公式an,1、一(n)當q-時,試證實a1a23an1Sn3n1.2Snn29n.3annlog32.4an2.錯位相減法求和1.an2n13n,求Sn2n23.an3n12,求Sn2.an2n3n,求Sn4.數(shù)列an的前n項和Sn

2、ann21,數(shù)列bn滿足3nbn1(n1)an1nan,(I)求an,bn(n)設n為數(shù)列bn的前n項和,求Tn.5.設等比數(shù)列an的前項和為Sn,an12Sn2(I)求數(shù)列an的通項公式(n)在an和an1之間插入n個數(shù),使這n2個數(shù)組成公差為dn的等差數(shù)列,求數(shù)列1dn前n項和Tn6.數(shù)列an滿足：Sn_*.一、_-.1an(nN),其中Sn為數(shù)列an的刖n項和.(I)試求an的通項公式(n)假設數(shù)列bn滿足：bn3nN),求bn的前n項和公式Tn7.正項等比數(shù)列an的前n項和為Sn,a416,且a2,a3的等差中項為S2.(I)求數(shù)列an的通項公式(n)設n,求bn的前n項和公式Tna2

3、n11Sn3n1.2Sn-123n11n1115n,Tndn43168163o,3n2n24n3n1.3Sn4.4an2n1,bn7.5an23,2333n1n1n3.6an2,Tnn12n127an2,Tn993.裂項法求和,一,1(1)an為等差數(shù)列,anan1111anan1danan通項公式,求前n項和Sn1.an2.3.4.5.6.7.8.9.anananananananan10.a2n12n13n13n23n23n124n216n32n1Sn1n1-n2n2n12n11SnSnSnSnSnSnSnSnSnSn4n11.an-二43433.數(shù)列an的前n項和為Sn,且滿足an-Sn2

4、(i)求數(shù)列an的通項公式(n)假設bn10g2an,且品bnbn2求數(shù)列Cn的前n項和Tn4.數(shù)列an滿足ai1,aia?*anian1.n2,nN(I)求數(shù)列an的通項公式an(n)設bnu,求數(shù)列an1an11bn的前項和Tnc1111Sn1J12a4n31n13-.12021.299.3an2,Tn4322n1.4an2,bn21715b4.分組法求和.1,1r11.求數(shù)列的前n項和：11,-4,7,fy3n22222n13.an是首項為19,公差為2的等差數(shù)列(I)求通項an(n)設bnan是首項為1,公比為3的等比數(shù)列,求數(shù)列bn的通項公式及其前n項和4.求和：等差數(shù)列an中,a3

5、5,65225(1)求通項an及Sna(n)設bn2n2n3,求數(shù)列bn的前n項和Sn1Sn-.2Sn2n2nn1_n11.3an212n,bn212n3Tn20nn21.4Sn2n122n.5Snnn3In31,n2k2n13nIn3In21,n2k122021高考數(shù)學專題復習：分類討論5 .等差數(shù)列an的前n項和為Sn,且a65,S462.(I)求斗通項公式(n)求數(shù)列|an|的前n項和Tn6 .數(shù)列an中,a11,a24,anan22,n3(I)求an通項公式(n)求數(shù)列4的前n項和Sn8.等差數(shù)列an的前n項和為Sn,且a12,4Snanan1,nN(I)求an通項公式1,、,一_n_

6、1(n)設數(shù)列的前n項和Tn,求證：Tnan2n4n429.等差數(shù)列an的前n項和為Sn,且Sn2ann23n2(I)求證：數(shù)列an2n為等比數(shù)列(n)設bnancosn,求數(shù)列bn的前n項和Tn.4Sn2n1.n2k15an3n23.Tn2n.n2k43n.26an77n.n2k1n2.n2kn23n2n2n23n.n22k2k1.n2k17ann.n2k8an2n.bn112.4n4nnbn14nn1Tn11114n444n1.9q2bn2n222-.n2k2n12.n32k2021高考數(shù)學專題復習：等差等比證實1 .等差數(shù)列證實：an1and(常數(shù))an2 .等比數(shù)列的證實方法：亙q(常

7、數(shù))練習:1.在數(shù)列an中,ai3,an15an4(i)求證：數(shù)列an1是等比數(shù)列(n)求數(shù)列an的通項公式an及前n項和Sn2.數(shù)列an滿足：ai1,a22自2anan1(I)求證：an1an是等比數(shù)列(n)求數(shù)列an的通項公式ann*3 .數(shù)列an滿足a11,且an2an12(n2,且nN).a(i)證實數(shù)列4-是等差數(shù)列2n(n)求數(shù)列an的通項公式an及前n項之和Sn4 .設數(shù)列an的前n項和為Sn,a11,&14%2(I)設bnan12an,證實數(shù)列bn是等比數(shù)列(n)求an5 .數(shù)列an的前n項和&滿足Sn2an(1)n,n1.2(I)求證數(shù)列an-(1)n為等比數(shù)列3(n)求an

8、及前n項和Sn6 .數(shù)列an的前n項和Sn滿足Sn1a2sla1,其中a20,求證：an是首項為1的等比數(shù)列n7 .數(shù)列an中,a15且an2an121n2且nN.(I)證實：數(shù)列a二為等差數(shù)列2n(n)求數(shù)列an的前n項和Sn8.設數(shù)列an的前n項和為Sn,a14,an1Sn3n,bnS3n(I)求證：數(shù)列bn為等比數(shù)列,并求bn的通項公式(n)令Cn2log2bnnbn2,求數(shù)列c的前n項和Tn、_一,、,一一*、9 .在數(shù)列an中,311,an2(an11)n(n2,nN)(i)證實：數(shù)列ann是等比數(shù)列(n)求數(shù)列an的通項公式an及前n項之和Sn13a10 .a1-,an12an3(

9、I)證實:1數(shù)列是等差數(shù)列an(n)設fnan,求fn的最大值11 .假設數(shù)列an的前n項之和為Sn2an4,bn1an2bn,且42(i)求an(n)求bn的前n項和Tn1.12 .數(shù)列an中,a11,n2時,an,Sn,Sn3成等比數(shù)列求an的刖n項之和Sn及通項公式an1(i)求證：一是等差數(shù)列Sn(n)求an13 .設實數(shù)數(shù)列an的前n項和Sn,滿足ai1,Snnan2nn1(i)求證an為等差數(shù)列,并求an和Sn1(n)設數(shù)列的刖項和為Tn,試求Tn的取值范圍anan14,an5n11,Sn5n1.2bn1.3d1,Sn2n32n3.4q2,an3n12n29q2,an2n1n.6q

10、a2.7bn1,Snn2n1n.8q2,bn2n1,Sn2,an2nn,Sn2nn4/c.10anl11a2n1,bnn2n.Tnn2n12.1,n112d2,bn2n12no.13an2n1,Snn2,bn22n12n/n2n12021高考數(shù)列復習測試題一.選擇題：1.公比為2等比數(shù)列an的各項都是正數(shù),且a3ali16,那么log2a0()(A)4(B)5(C)(D)2.等差數(shù)列an中,aa510,a47,那么數(shù)列an的公差為A.1B.2C.33.定義在(,0)U(0,)上的函數(shù)f(x),如果對于任意給定的等比數(shù)列an,f(an)仍是等比數(shù)列,那么稱f(x)為“保等比數(shù)列函數(shù).現(xiàn)有定義在(

11、,0)U(0,)上的如下函數(shù):f(x)x2;f(x)2xf(x)VFx|；f(x)ln|x|.那么其中是“保等比數(shù)列函數(shù)的f(x)的序號為4.an為等比數(shù)列,a4a7(A)(B)(C)(D)55.在等列an中,a4+a8=1611項和Sii=58B.176C.143886.等差數(shù)列an的前n項和為Sn,a55,Ss15,那么數(shù)列的前100項和為anan199A.101100B.101C.99100101D.1007.數(shù)列an的首項為3,H為等差數(shù)列且bnan.假設那么b3ZD.12,那么a8A.3B.0C.8D.118.數(shù)列an的前項和Sn滿足SnSmSnm,且a11.那么a10A.B.9C.

12、109.an為等差數(shù)列,其公差為a7是a3與a的等比中項,Sn為an的前n項S10A.110B.90C.1109010.有一個奇數(shù)組成的數(shù)陣排列如下:21i-II17那么第30行從左到右第3個數(shù)是A.1125B.3215C.1310D.1051二.填空題:11.設數(shù)列an中,a12,an1ann1,那么通項an12.遞增的等差數(shù)列an滿足a1.21,a3a24,貝Uan15.數(shù)列an滿足a13am4an2_,小mm、一n一,求an的通項公式an12三.解做題：22a16.數(shù)列an的首項a,一,an1-,n1,2,3,.3an1一1、(I)證實：數(shù)列一1是等比數(shù)列an(n)數(shù)列2的前n項和5.a

13、n1217.數(shù)列an的前n項和Sn-n2kn(kN),且Sn的最大值為82(i)確定常數(shù)k,求an92a-(n)求數(shù)列一T的前n項和Tn公f(x)18.dx,：,13(x0)成等差數(shù)列.又數(shù)列an(an0)中,a13,此數(shù)列的前n項的和Sn對所有大于1的正整數(shù)n都有Snf(Sn1).(I)求數(shù)列an的第n1項11.(n)假設；bn是,一的等比中項,且Tn為bn的前n項和,求Tn-an1an19 .an是等差數(shù)列,其前n項和為Sn,bn是等比數(shù)列,且ai=b1二2,a4+b4=27,Gb4=10.(I)求數(shù)列an與bn的通項公式(口)記Tnanbianib2an2b3Laibn,求Tn220 .等差數(shù)列an為遞增數(shù)列,且a2,a5是方程x12x270的兩根,數(shù)列bn的前n項一,1,和Tn1bn;2(I)求數(shù)列an和bn的通項公式升3nbn,-(n)右Cn,求數(shù)列Cn的刖n項和Sn.anan121.設數(shù)列an)的前n項和為Sn,滿足2Snan一n1*一一,121(nN),且a1,a25,a3成等差數(shù)列.(I)求