2021年高中数学必修五知识点公式总结.pdf

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2021年高中数学必修五知识点公式总结.pdf

-.-.word.zl.必修五数学公式概念第一章解三角形1.1 正弦定理和余弦定理1.1.1 正弦定理1、正弦定理：在一个三角形中，各边和它所对角的正弦的比相等，即sinsinsinabcABC.正弦定理推论：2sinsinsinabcRABCR为三角形外接圆的半径2 sin,2sin,2sinaRA bRBcRCsinsinsin,sinsinsinaAbBaAbBcCcC:sin:sin:sina b cABCsinsinsinsinsinsinabcabcABCABC2、解三角形的概念：一般地，我们把三角形的各个角即他们所对的边叫做三角形的元素。任何一个三角形都有六个元素：三条边),(cba和三个内角),(CBA.在三角形中，三角形的几个元素求其他元素的过程叫做解三角形。3、正弦定理确定三角形解的情况图形关系式解的个数A为锐角sinabAab一解sinbAab两解sinabA无解A为钝角或直角ba一解ba无解|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 1 页，共 9 页-.-.word.zl.4、任意三角形面积公式为：2111sinsinsin2224()()()()2sinsinsin2ABCabcSbcAacBabCRrp papbpcabcRABC1.1.2 余弦定理5、余弦定理：三角形中任何一边的平方等于其他两边的平方的和减去这两边与它们的夹角的余弦的积的两倍，即2222cosabcbcA，2222cosbaccaB，2222coscababC.余弦定理推论：222cos2bcaAbc，222cos2acbBac，222cos2abcCab6、不常用的三角函数值1575105165sin426426426426cos426426426426tan323232321.2 应用举例1、方位角：如图1，从正北方向顺时针转到目标方向线的水平角。2、方向角：如图2，从指定线到目标方向线所成的小于90的水平角。指定方向线是指正北或正南或正西或正东3、仰角和俯角：如图3，与目标线在同一铅垂平面内的水平视线和目标视线的夹角，目标视线在水平视线上方时叫做仰角，目标视线在水平视线下方时叫做俯角。1方位角2方向角3仰角和俯角 4视角4、视角：如图4，观察物体的两端，视线张开的角度称为视角。5、铅直平行：于海平面垂直的平面。6、坡角与坡比：如图5，坡面与水平面所成的夹角叫坡角，坡面的铅直|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 2 页，共 9 页文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3-.-.word.zl.高度与水平宽度的比叫坡比hil.5坡角与坡比第二章数列2.1 数列的概念与简单表示法1、数列的定义：按照一定顺序排列的一列数称为数列。数列中的每一个数都叫做这个数列的项。数列中的每一项和它的序号有关，排在第一位的数称为这个数列的第1 项也叫首项，排在第二位的数称为这个数列的第2 项，排在第n位的数称为这个数列的第n项。所以，数列的一般形式可以写成1a，2a，3a，na，简记为na.2、数列的通项公式：如果数列na的第n项与序号n之间的关系可以用一个式子来表示，那么这个公式叫做这个数列的通项公式。3、数列的递推公式：如果数列的第1 项或前几项，且从第 2 项或某一项开场的任一项na与它的前一项1na或前几项 2n间的关系可以用一个公式表示，那么这个公式叫做这个数列的递推公式。定义式为121nnaa1n4、数列与函数：数列可以看成以正整数集*N或它的有限子集1,2,3,4,n,为定义域的函数nfan，当自变量按照从大到小的顺序依次取值时，所对应的一列函数值。通项公式可以看成函数的解析式。5、数列的单调性：假设数列na满足：对一切正整数n，都有1nnaa或1nnaa，那么称数列na为递增数列或递减数列。判断方法：转化为函数，借助函数的单调性，求数列的单调性；作差比拟法，即作差比拟1na与na的大小；2.2 等差数列1、等差数列的定义：一般地，如果一个数列从第2 项起，每一项与它的前一项的差等于同一个常数，那么这个数列就叫做等差数列，这个常数叫做等差数列的公差，公差常用字母d表示。定义式为daann12n，n*N或daann 1n*N2、等差中项：由三个数a，A，b组成的等差数列可以看成最简单的等差数列。这时，A叫做a与b的等差中项。A是a，b的等差中项2baAbaA2AbaA.|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 3 页，共 9 页文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 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HM1H2M9O1Y3 ZT3G1A3L5T3-.-.word.zl.3、等差中项判定等差数列：任取相邻的三项1na，na，1nann,2*N，那么1na，na，1na成等差数列112nnnaaa2nna是等差数列。4、等差数列的通项公式11naand，其中1a为首项，d为公差。变形为：11naadn.5、通项公式的变形：dmnaamn，其中ma为第m项。变形为mnaadmn.6、等差数列的性质：1 假设n，m，p，q*N，且qpnm，那么qpnmaaaa；2假设pnm2，那么pnmaaa2；（3）假设m，p，n成等差数列，那么ma，pa，na成等差关系；（4）假设na成等差数列qpnan公差为p，首项为qp；（5）假设nc成等差数列，那么na也成等差数列；（6）如果nanb都是等差数列，那么qpan，mnqbpa也是等差数列。2.3 等差数列的前n项和1、一般数列na与ns的关系为2111nSSnSannn.2、等差数列前n项和的公式：dnnnaaanSnn212113、等差数列前n项和公式的函数特征：1由ndanddnnnaSn2221121，令2dA，21daB，那么na为等差数列nnBAnS2BA、为常数，其中Ad2，baa1.假设0A，即0d，那么nS是关于n的无常数项的二次函数。假设0A，即0d，那么1naSn.2假设na为等差数列，nSn也是等差数列，公差为2d3假设na为等差数列，,232,kkKkkSSSSS也成等差数列4假设mSn，nSm，那么nmSnm5假设nmSS，那么0nmS|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 4 页，共 9 页文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3-.-.word.zl.6假设nnba是均为等差数列，前n项和分别是nA与nB，那么有1212mmmmBAba7在等差数列na中，01a，0d，那么nS存在最大值，01a，0d，那么nS存在最小值。2.4 等比数列1、等比数列：一般地如果一个数列从第2 项起，每一项与它前一项的比等于同一常数，那么这个数列叫做等比数列，这个常数叫做等比数列的公比，公比通常用字母q表示0q.定义式：1nnaqa，(2n,0na,0q).2、等比中项：如果在a与b中间插入一个数G，使a，G，b成等比数列，那么G叫做a与b的等比数列。a，G，b成等比数列2GbGabGabaG.两数同号才有等比中项，且有2 个互为相反数。3、通项公式：111nnnaaa qqq其中首相为1a，公比为q.4、等比数列的性质：n mnmaa qn，m*N.2.5 等比数列的前n项和1、等比数列的前n项和的公式：11111111nnnnaqSaqaa qqqq2、等比数列的前n项和的函数特征：当1q时，1111111nnnaqaaSqqqq.记11aAq，即nnSAqA.3、等比数列的前n项和的性质：在等比数列中：1当kS，2kkSS，32kkSS，均不为零时，数列成等差数列。公比为qk.2nmn mnmmnSSq SSq S3m nmnaqa或m nmnaaqm、n*N4假设mnpq，那么mnpqaaaa|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 5 页，共 9 页文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3-.-.word.zl.5假设na为等差数列，那么naC为等比数列6假设na为正项等比数列，那么logCna是等差数列7 假设na、nb均为等比数列，那么0knnnnnnnnaaaaabab、等仍是等比数列。公比分别为：11221kqqqqq qqq、.8 等比数列na的增减性：当101aq，或1001aq时，na为递增数列；当1001aq或101aq时，na为递增减数列。4、由递推公式求数列通向法：1累加法：1nnaaf n变形：1nnaaf n2累乘法：1nnaafn变形：1nnafna3取倒数法：1nnnpaaqap4构建新数列法：1nnapaq其中p，q均为常数，(1)0pq p设1nnakp aknak为等比数列。第三章不等式3.1 不等式关系与不等式1、不等式定义：用不等号、表示不等关系的式子叫不等式，记作fxg x，fxg x等。用“或“连接的不等式叫严格不等式，用不“或“连接的不等式叫非严格不等式。2、实数的根本性质0baba；0baba；0baba.实数的其他性质0,000abbaba；0,000abbaba；000abba|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 6 页，共 9 页文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3-.-.word.zl.3、不等式的根本性质1对称性：abba2传递性：cacbba,3可加性：cbcaba推论 1：bcacba移向法那么推论 2：dbcadcba同向不等式的相加法那么4可乘性：0abacbcc；0abacbcc5同向相加：abacbdcd；异向可减：abadbcdc6同向可乘：00abacbdcd；异项可除：00ababdcdc7乘方法那么：0abnnabnN，1n8可开方性法那么：0nnababnN，2n9倒数法那么：110ababab3.2 一元二次不等式及其解法1、一元二次不等式定义：我们把只含有一个未知数，并且未知数的最高次数是2的不等式，称为一元二次不等式。使一元二次不等式成立的未知数的值叫做这个一元二次不等式的解，一元二次不等式的所有解组成的集合，叫做这个一元二次不等式的解集。2、二次函数，一元二次方程，一元二次不等式三者之间的关系24bac00020axbxc0a的图像20axbxc0a的根两个不相等的实数根12xx两个相等的实数根12xx没有实数根20axbxc0a的解集12x xxxx或2bx xaR|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 7 页，共 9 页文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 HM1H2M9O1Y3 ZT3G1A3L5T3文档编码:CX10X7K3D10R8 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