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数列的极限课件数列的极限课件R正六边形的面积正六边形的面积1A正十二边形的面积正十二边形的面积2A正正 形的面积形的面积126 nnA,321nAAAAS说明:刘徽从圆内接正六边形,逐次边数加倍到正说明:刘徽从圆内接正六边形,逐次边数加倍到正3072边形得到圆周率边形得到圆周率 的近似值为的近似值为3.14161 1 111, , , ,2 4 82n5161611.53 102a3110010017.89 102ay0.50.450.40.350.30.250.20.150.10.05 0 1 2 3 4 5 6 7 8 9 10 x 12nna 0nana na na nalimnnaA231 111,2 222n12n1lim02nn231111,10 101010n110n1lim010nnlim0nnq1q 1 1 111, , , , ,2 3 4n1n1lim0nny10.90.80.70.60.50.40.30.20.1 0 2 4 6 8 10 12 14 16 18 20 x 1nan01lim0nn2,2,2,2,lim22nlim0(C)nC为常数lim0nnq1q 1lim0nn1,1,nnnannn是奇数是偶数0.3,0.33,0.333,0.3333,n 个1111, ,23nn1nn1lim0nnn1nnan12131811416151701距离量化:距离量化: ,随着,随着n n的增大,的增大, 的值的值越来越小,无限趋近于越来越小,无限趋近于0 0,即,即1100nnann1n00na nalimnnaAnaAlim0nnaA21nnan21925,1, ,4,4444n1,1, 1,1,1 ,n3, 3, 3, 3, 2yxxy2yxxy2yxxy2222223321112111211 2161 216nnSnnnnnnnnn nnnnnn 21 21limlim6nnnnnSSn=?lim,limnnnnaAbBlimlimlimnnnnnnnababA Blimlimlimnnnnnnna babA BlimlimlimnnnnnC aCaC Alim,limnnnnaAbBlimlim0limnnnnnnnaaABbbB2lim 7nn34limnnn21 21lim6nnnn34lim3nnn2221 212311limlim366nnnnnnnn分子最高次项系数分母最高次项系数32231lim6nnnn23231lim6nnnn222214732limnnnnnn23134lim43nnnnn
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