17極限

1、九、微積分1.極限知識(shí)網(wǎng)絡(luò)極限結(jié)構(gòu)簡(jiǎn)圖畫龍點(diǎn)晴概念數(shù)列的極限:是一個(gè)無(wú)窮數(shù)列是一個(gè)常數(shù)如果對(duì)于預(yù)先給定的任意小的正數(shù)總存在正nanaa?整數(shù)N使得只要正整數(shù)就有||0由得..21|2121|||nnnaan????????n21?21?n取N=[]當(dāng)時(shí)所以?21Nn???????|2121|||nnaan.2121lim?????nnn[例2]利用極限有定義證明.1)121(lim?????nn[題解]任給0由得..21|1121|||

2、nnnaa????????n21?1log2?n取N=[]當(dāng)時(shí)恒成立所以?1log2Nn???????|1121|||nnaa.1)121(lim?????nn公式數(shù)列極限的四則運(yùn)算法則：如果an=abn=b那么??nlim??nlim（2）由題意得(1kan)=1k0，an=0，即()n1=0，??nlim?????nlim??nlimk?111?kk由此可知0q且p≠1q≠1.設(shè)cn=anbnsn為數(shù)列｛cn｝的前n項(xiàng)和.求.1li

3、m???nnnSS[題解])1)(1()1)(1()1)(1()1)(1(1)1(1)1(111111111????????????????????nnnnnnnnnqpbpqaqpbpqaSSqqbppaS下面分兩種情況討論.(Ⅰ)當(dāng)p1時(shí)，pq001?pqpqaqapppqpbpqappqpbpqapppqpbpqapppqpbpqapSSnnnnnnnnnnnnnnnnnnnnnnn????????????????????????