高中數(shù)學(xué) 第三章 數(shù)學(xué)歸納法與貝努利不等式 3.2 用數(shù)學(xué)歸納法證明不等式貝努利不等式課件 新人教B版選修45

《高中數(shù)學(xué) 第三章 數(shù)學(xué)歸納法與貝努利不等式 3.2 用數(shù)學(xué)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(huì)員分享，可在線閱讀，更多相關(guān)《高中數(shù)學(xué) 第三章 數(shù)學(xué)歸納法與貝努利不等式 3.2 用數(shù)學(xué)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(yè)珍藏版）》請(qǐng)?jiān)谘b配圖網(wǎng)上搜索。

1、3 3.2 2用數(shù)學(xué)歸納法證明不等式用數(shù)學(xué)歸納法證明不等式,貝努利不貝努利不等式等式目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重

2、難聚焦ZHISHISHULI知識(shí)梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航1.會(huì)用數(shù)學(xué)歸納法證明簡(jiǎn)單的不等式.2.會(huì)用數(shù)學(xué)歸納法證明貝努利不等式.3.了解貝努利不等式的應(yīng)用條件.目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUIT

3、ANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航1.用數(shù)學(xué)歸納法證明不等式在不等關(guān)系的證明中,有多種多樣的方法,其中數(shù)學(xué)歸納法是最常用的方法之一,在運(yùn)用數(shù)學(xué)歸納法證不等式時(shí),推導(dǎo)“k+1”成立時(shí),比較法、分析法、綜合法、放縮法等方法常被靈活地應(yīng)用.【做一做1-1】 欲用數(shù)學(xué)歸納法

4、證明:對(duì)于足夠大的正整數(shù)n,總有2nn3,n0為驗(yàn)證的第一個(gè)值,則()A.n0=1B.n0為大于1小于10的某個(gè)整數(shù)C.n010D.n0=2解析:n=1時(shí),21;n=2時(shí),48;n=3時(shí),827;n=4時(shí),1664;n=5時(shí),32125;n=6時(shí),64216;n=7時(shí),128343;n=8時(shí),256512;n=9時(shí),5121 000.故選C.答案:C目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦Z

5、HISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航【做一做1-2】 用數(shù)學(xué)歸納法證明“ nN*,n1)”時(shí),由n=k(k1)不等式成立推證n=k+1時(shí),左邊應(yīng)增加的項(xiàng)數(shù)是()A.2k-1B.2k-1C.2kD

6、.2k+1解析:增加的項(xiàng)數(shù)為(2k+1-1)-(2k-1)=2k+1-2k=2k.答案:C目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJI

7、AO重難聚焦ZHISHISHULI知識(shí)梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航2.用數(shù)學(xué)歸納法證明貝努利不等式(1)定理1(貝努利不等式):設(shè)x-1,且x0,n為大于1的自然數(shù),則(1+x)n1+nx.(2)定理2:設(shè)為有理數(shù),x-1,若01,則(1+x)1+x;若1,則(1+x)1+x.當(dāng)且僅當(dāng)x=0時(shí)等號(hào)成立.名師點(diǎn)撥當(dāng)指數(shù)推廣到任意實(shí)數(shù)且x-1時(shí),若01,則(1+x)1+x;若1,則(1+x)1+x.當(dāng)且僅當(dāng)x=0時(shí)等號(hào)成立.目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANX

8、I隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISH

9、ISHULI知識(shí)梳理目標(biāo)導(dǎo)航應(yīng)用數(shù)學(xué)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(xué)歸納法證明不等式的問(wèn)題中,從“n=k”到“n=k+1”的過(guò)渡,利用歸納假設(shè)是比較困難的一步,它不像用數(shù)學(xué)歸納法證明恒等式問(wèn)題一樣,只需拼湊出所需要的結(jié)構(gòu)來(lái),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(shí)也行不通,因?yàn)閷?duì)不等式來(lái)說(shuō),它還涉及“放縮”的問(wèn)題,它可能需通過(guò)“放大”或“縮小”的過(guò)程,才能利用上歸納假設(shè),因此,我們可以利用“比較法”“綜合法”“分析法”等來(lái)分析從“n=k”到“n=k+1”的變化,從中找到“放縮尺度”,準(zhǔn)確地拼湊出所需要的結(jié)

10、構(gòu).目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理DIANLITOUXI典例透析SUITANG

11、LIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航題型一題型二題型三用數(shù)學(xué)歸納法證明數(shù)列型不等式 (1)求數(shù)列an的通項(xiàng)公式;(2)求證:對(duì)一切正整數(shù)n,不等式a1a2an12=1;當(dāng)n=2時(shí),22=4=22;當(dāng)n=3時(shí),23=852=25;當(dāng)n=6時(shí),26=6462=36.故猜測(cè)當(dāng)n5(nN*)時(shí),2nn2.下面用數(shù)學(xué)歸納法進(jìn)行證明:(1)當(dāng)n=5時(shí),顯然成立.(2)假設(shè)當(dāng)n=k(k5,且kN*)時(shí),不等式成立,即2kk2(k5),則當(dāng)n=k+1時(shí),2k+1=22k2k2=k2+k2+2k+1-2k-1=(k+1)2+(k-1)2-2(k+1)2(

12、因?yàn)?k-1)22).目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理DIANLITOUXI典例

13、透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航題型一題型二題型三反思利用數(shù)學(xué)歸納法比較大小,關(guān)鍵是先用不完全歸納法歸納出兩個(gè)量的大小關(guān)系,猜測(cè)出證明方向,再利用數(shù)學(xué)歸納法證明結(jié)論成立.目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練Z

14、HONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航題型一題型二題型三用數(shù)學(xué)歸納法證明探索型不等式 目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練Z

15、HONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航題型一題型二題型三(1)當(dāng)n=1時(shí),顯然成立.(2)假設(shè)當(dāng)n=k(kN*,且k1)時(shí),目標(biāo)導(dǎo)航DIANLITOUXI典例透

16、析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJU

17、JIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航題型一題型二題型三反思用數(shù)學(xué)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(guò)觀察部分項(xiàng)的特點(diǎn)進(jìn)行歸納,判斷并猜測(cè)出一般結(jié)論,然后用數(shù)學(xué)歸納法進(jìn)行證明.目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦Z

18、HISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航1 2 3 41下列選項(xiàng)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(yàn)證即可.答案:C目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIA

19、O重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航1 2

20、3 4答案:C 目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理DIANLITOUXI典例透析S

21、UITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航1 2 3 4目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識(shí)梳理目標(biāo)導(dǎo)航1 2 3 4