级数2N次方乘以(sin3的n次方分之π) 具体用比值判别法怎么求它的敛散性

分类: 作业答案 • 2022-02-05 22:45:03

问题描述：

答

lim[2^(n+1)sin(π/3^(n+1))]/[2^(n)sin(π/3^(n)]
=2limsin(π/3^(n+1))]/[sin(π/3^(n)]
=2limsin(π/3^(n+1))]/[sin(π/3^(n)]
=2limπ/3^(n+1)/[(π/3^(n)]
=2/3