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_数学解答

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

人气：289 ℃　时间：2020-05-29 20:27:03

解答

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<1,级数收敛