n趋向无穷,lim根号2n+根号3n/根号下2n-根号下3n,其中2n,3n是2的n次方和3的n次方.

题目

n趋向无穷,lim根号2n+根号3n/根号下2n-根号下3n,其中2n,3n是2的n次方和3的n次方.

答案

根号2n+根号3n/根号下2n-根号下3n
=[根号(2/3)^n+1]/[根号(2/3)^n-1]
n趋向无穷,根号(2/3)^n趋于0
lim...=1/(-1)=-1