《高中數(shù)學 第三章 數(shù)學歸納法與貝努利不等式 3.2 用數(shù)學歸納法證明不等式貝努利不等式課件 新人教B版選修45》由會員分享，可在線閱讀，更多相關《高中數(shù)學 第三章 數(shù)學歸納法與貝努利不等式 3.2 用數(shù)學歸納法證明不等式貝努利不等式課件 新人教B版選修45（20頁珍藏版）》請在裝配圖網(wǎng)上搜索。
1、3 3.2 2用數(shù)學歸納法證明不等式用數(shù)學歸納法證明不等式,貝努利不貝努利不等式等式目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重
2、難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航1.會用數(shù)學歸納法證明簡單的不等式.2.會用數(shù)學歸納法證明貝努利不等式.3.了解貝努利不等式的應用條件.目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUIT
3、ANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航1.用數(shù)學歸納法證明不等式在不等關系的證明中,有多種多樣的方法,其中數(shù)學歸納法是最常用的方法之一,在運用數(shù)學歸納法證不等式時,推導“k+1”成立時,比較法、分析法、綜合法、放縮法等方法常被靈活地應用.【做一做1-1】 欲用數(shù)學歸納法
4、證明:對于足夠大的正整數(shù)n,總有2nn3,n0為驗證的第一個值,則()A.n0=1B.n0為大于1小于10的某個整數(shù)C.n010D.n0=2解析:n=1時,21;n=2時,48;n=3時,827;n=4時,1664;n=5時,32125;n=6時,64216;n=7時,128343;n=8時,256512;n=9時,5121 000.故選C.答案:C目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦Z
5、HISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航【做一做1-2】 用數(shù)學歸納法證明“ nN*,n1)”時,由n=k(k1)不等式成立推證n=k+1時,左邊應增加的項數(shù)是()A.2k-1B.2k-1C.2kD
6、.2k+1解析:增加的項數(shù)為(2k+1-1)-(2k-1)=2k+1-2k=2k.答案:C目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJI
7、AO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航2.用數(shù)學歸納法證明貝努利不等式(1)定理1(貝努利不等式):設x-1,且x0,n為大于1的自然數(shù),則(1+x)n1+nx.(2)定理2:設為有理數(shù),x-1,若01,則(1+x)1+x;若1,則(1+x)1+x.當且僅當x=0時等號成立.名師點撥當指數(shù)推廣到任意實數(shù)且x-1時,若01,則(1+x)1+x;若1,則(1+x)1+x.當且僅當x=0時等號成立.目標導航DIANLITOUXI典例透析SUITANGLIANX
8、I隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISH
9、ISHULI知識梳理目標導航應用數(shù)學歸納法證明不等式,從“n=k”到“n=k+1”證明不等式成立的技巧有哪些?剖析:在用數(shù)學歸納法證明不等式的問題中,從“n=k”到“n=k+1”的過渡,利用歸納假設是比較困難的一步,它不像用數(shù)學歸納法證明恒等式問題一樣,只需拼湊出所需要的結(jié)構(gòu)來,而證明不等式的第二步中,從“n=k”到“n=k+1”,只用拼湊的方法,有時也行不通,因為對不等式來說,它還涉及“放縮”的問題,它可能需通過“放大”或“縮小”的過程,才能利用上歸納假設,因此,我們可以利用“比較法”“綜合法”“分析法”等來分析從“n=k”到“n=k+1”的變化,從中找到“放縮尺度”,準確地拼湊出所需要的結(jié)
10、構(gòu).目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANG
11、LIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航題型一題型二題型三用數(shù)學歸納法證明數(shù)列型不等式 (1)求數(shù)列an的通項公式;(2)求證:對一切正整數(shù)n,不等式a1a2an12=1;當n=2時,22=4=22;當n=3時,23=852=25;當n=6時,26=6462=36.故猜測當n5(nN*)時,2nn2.下面用數(shù)學歸納法進行證明:(1)當n=5時,顯然成立.(2)假設當n=k(k5,且kN*)時,不等式成立,即2kk2(k5),則當n=k+1時,2k+1=22k2k2=k2+k2+2k+1-2k-1=(k+1)2+(k-1)2-2(k+1)2(
12、因為(k-1)22).目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例
13、透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航題型一題型二題型三反思利用數(shù)學歸納法比較大小,關鍵是先用不完全歸納法歸納出兩個量的大小關系,猜測出證明方向,再利用數(shù)學歸納法證明結(jié)論成立.目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練Z
14、HONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航題型一題型二題型三用數(shù)學歸納法證明探索型不等式 目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練Z
15、HONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航題型一題型二題型三(1)當n=1時,顯然成立.(2)假設當n=k(kN*,且k1)時,目標導航DIANLITOUXI典例透
16、析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJU
17、JIAO重難聚焦ZHISHISHULI知識梳理目標導航題型一題型二題型三反思用數(shù)學歸納法解決探索型不等式的思路是:觀察歸納猜想證明,即先通過觀察部分項的特點進行歸納,判斷并猜測出一般結(jié)論,然后用數(shù)學歸納法進行證明.目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦Z
18、HISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航1 2 3 41下列選項中,不滿足12+23+34+n(n+1)3n2-3n+2的自然數(shù)n是()A.1B.1,2C.1,2,3 D.1,2,3,4解析:將n=1,2,3,4分別代入驗證即可.答案:C目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIA
19、O重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航1 2
20、3 4答案:C 目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析S
21、UITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航1 2 3 4目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航1 2 3 4
高中數(shù)學 第三章 數(shù)學歸納法與貝努利不等式 3.2 用數(shù)學歸納法證明不等式貝努利不等式課件 新人教B版選修45
