2022年2020版高考数学新增分大一轮浙江专用版精编讲义：第七章数列与数学归纳法高考专题突破四Word版含解析 .pdf

名校名师推荐1 高考专题突破四高考中的数列问题题型一等差数列、等比数列的基本问题例 1(2018 浙江杭州地区四校联考)已知数列 an满足 a11,1a2n41an1，记 Sna21a22 a2n，若 S2n1 Snt30对任意的nN*恒成立(1)求数列 a2n 的通项公式；(2)求正整数t 的最小值解(1)由题意得1a2n11a2n4，则1a2n是以 1 为首项，4 为公差的等差数列，则1a2n1(n1)44n3，则 a2n14n3.(2)不妨设 bnS2n1Sna2n1a2n2a22n1，考虑到 bnbn1a2n1a2n2a22n1(a2n2a2n3 a22n2a22n3)a2n1a22n2a22n314n 118n 518n 918n 218n 518n 218n 90，因此数列 bn单调递减，则 bn的最大值为b1S3S1a22a2315191445t30，t283，则 tmin10.思维升华等差数列、等比数列综合问题的解题策略(1)分析已知条件和求解目标，为最终解决问题设置中间问题，例如求和需要先求出通项、求通项需要先求出首项和公差(公比)等，确定解题的顺序(2)注意细节：在等差数列与等比数列综合问题中，如果等比数列的公比不能确定，则要看其是否有等于1 的可能，在数列的通项问题中第一项和后面的项能否用同一个公式表示等，这些细节对解题的影响也是巨大的名校名师推荐2 跟踪训练1(2018 浙江名校联盟联考)已知等差数列 an的前 n 项和为 Sn，等比数列 bn 的公比是 q(q1)，且满足：a12，b11，S23b2，a2 b3.(1)求 an与 bn；(2)设 cn2bn 23na，若数列 cn是递减数列，求实数 的取值范围解(1)设数列 an的公差为d，依题意可得22d3q，2dq2，解得d 1，q 1(舍去)或d2，q2.故 an 22(n1)2n，bn2n1.(2)由(1)可知 cn2n 3n，若cn是递减数列，则cn1cn，即 2n1 3n11223n在 n N*时成立，只需 1223nmax.因为 y1223n在 nN*时单调递减，所以1223nmax122313.故 13，即实数 的取值范围是13，.题型二数列的通项与求和例 2(2018 台州质检)已知数列 an的前 n 项和为 Sn，数列Snn是首项为1，公差为 2 的等差数列(1)求数列 an 的通项公式；(2)设数列 bn 满足a1b1a2b2anbn5(4n5)12n，求数列 bn的前 n 项和 Tn.解(1)因为数列Snn是首项为1，公差为 2 的等差数列，所以Snn12(n1)2n1.所以 Sn2n2n.当 n1 时，a1S11；当 n2 时，anSnSn1(2n2n)2(n1)2(n 1)4n3，当 n1 时，a11 也符合上式文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10名校名师推荐3 所以数列 an的通项公式为an4n3(nN*)(2)当 n 1 时，a1b112，所以 b12a12；当 n2 时，由a1b1a2b2anbn5(4n5)12n，所以a1b1a2b2an1bn15(4n1)12n1.两式相减，得anbn(4n3)12n.因为 an4n3，所以 bn4n34n312n2n(当 n1 时，也符合此式)又bn1bn2n12n2，则数列 bn 是首项为 2，公比为2 的等比数列所以 Tn2 12n122n12.思维升华(1)可以利用数列的递推关系探求数列的通项，利用递推关系构造数列或证明数列的有关结论(2)根据数列的特点选择合适的求和方法，常用的求和方法有错位相减法、分组转化法、裂项相消法等跟踪训练2(2018 浙江教育绿色评价联盟适应性考试)已知数列 an中，a13，a25，其前 n项和 Sn满足 SnSn2 2Sn12n1(n3)令 bn1an an1.(1)求数列 an 的通项公式；(2)若 f(x)2x1，求证：Tnb1f(1)b2f(2)bnf(n)16(n1)(1)解由题意知SnSn1Sn1Sn22n1(n3)，即 an an1 2n1(n3)，所以 an(anan1)(an1an2)(a3a2)a22n12n2 225 2n12n2 222 12 2n1(n3)，检验知 n1,2 时，结论也成立，故an2n1.(2)证明由于 bnf(n)12n 1 2n11 2n1122n1 1 2n12n1 2n1 1文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10名校名师推荐4 1212n112n11.故 Tnb1f(1)b2f(2)bnf(n)1212112211221123112n 112n111212112n111212116.所以 Tn16.题型三数列与不等式的交汇例 3已知数列 an 满足 a1 1，an1an1a2n，nN*，记 Sn，Tn分别是数列 an，a2n的前 n项和，证明：当nN*时，(1)an1an；(2)Tn1a2n12n1；(3)2n1Sn0，故 an1anan1a2nana3n1a2n0，an1an，n N*.(2)由1an11anan，得1a2n11a2na2n2，从而1a2n11a2n1a2n1 a2n221a21a21a22 a2n2n，又 a1 1，1a2n11a21a22a2n 2n，Tn1a2n12n1，nN*.(3)由(2)知，an11Tn2n 1，文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10名校名师推荐5 由 Tna211，得 an112n2，当 n2 时，an12n22 n2nn12(nn1)，Sna12(2 1)(32)(nn1)12(n1)2n，n2，又 a1 1，Sn2n1，综上，2n 1Snan；(2)12a213a31nan0，得 0an1.(1)a2nann 1，a2n1an1n11，两式相减得0a2n1a2nan1n1ann0，故 an1an0，即 an1an.(2)因为 anan1n1，所以1anan1n，由 0an1，得1an11n，文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10名校名师推荐6 从而当 i2 时，1i1ai1 1i11i 11i21i11i，ni11i1ai1 1a11ni21i1ai11a11ni21i11i1a11n1a1.所以12a213a31nan0；当 n6 时，cn0，设cn的前 n 项和为 Tn，则 Tn10nn2，当 n5 时，SnTn10n n2；当 n6 时，Sn2T5Tnn210n50.综上，Sn10nn2，n5，n210n50，n6.文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10名校名师推荐7 2(2018 绍兴市嵊州市适应性考试)已知 Sn是数列 an 的前 n 项和，a12，且 4Snan an1，数列 bn中，b114，且 bn1nbnn1 bn，nN*.(1)求数列 an 的通项公式；(2)设12332nnnbac(nN*)，求 cn的前 n 项和 Tn.解(1)当 n1 时，可得a24，当 n2 时，4Snan an1,4Sn1an an1，两式相减，得4anan(an1an1)，an0，an1an14，an的奇数项和偶数项分别成以4 为公差的等差数列，当 n2k1，kN*时，an2n；当 n2k，kN*时，an2n.an2n(nN*)(2)1bn1n1nbn1n，1n1 bn11nbn1n n 1，当 n2 时，1nbn1n1 bn11n11n，1n1 bn11n2 bn21n21n1，12b21b1 112，将上式累加得1nbn3n1n，bn13n 1(n2)，n1 时也适合，bn13n 1(nN*)，cnn2n，Tn12222323n12n1n2n，12Tn122223n12nn2n1，再由错位相减得Tn 2n22n.文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:CM4P9Z5L10G1 HH5Y2H10Q2N3 ZQ3V1E7P10R10文档编码:C