计算lim n→∞n
计算:lim n→∞n/(1+3+5+7……+(2n-1))计算：lim（1/3-1/9+1/27+……+（-1）^(n-1)*1/(3^n）]n→∞ 求下列极限:lim(1+2/3n)^(n+1)n→∞ lim(2n+3)/(2n+1)^(4n-1)n→∞
1 1/3，-1/9，1/27，……，（-1）^(n-1)*1/(3^n） 是无穷等比数列，首项1/3，公比-1/3 lim（1/3-1/9+1/27+……+（-1）^(n-1)*1/(3^n）] n→∞ =lim(1/3)[1-(-1/3)^n]/(1+1/3)n→∞ =(1/3)/(4/3)=1/4 2 lim(1+2/3n)^(n+1) n→∞ =lim([1+1/(3n/2)]^[2/3n])^(3/2)*(1+2/3n) n→∞ =e^(3/2) 3 lim(2n+3)/(2n+1)^(4n-1) n→∞ =lim([(1+3/2n)/(1+1/2n)]^4n/[(1+3/2n)/(1+1/2n)] n→∞ 其中(1+3/2n)^4n→[(1+3/2n)^(2n/3)]^6→e^6 (1+1/2n)^4n→[(1+1/2n)^(2n)]^2→e^2 所以原式=e^6/e^2=e^4。
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