lim(n->∞)n^2[x^(1/n)-x^(1/n+1)]答案是lnx没弄错。原题是x开n次方x开n＋1次方，没看懂

Question

lim(n->∞) n^2 [x^(1/n)-x^(1/n+1)]
答案是lnx
没弄错。原题是x开n次方 x开n＋1次方，
没看懂

Answer 1

哈哈
把x看成常量
1/n看作x1,1/(n+1)看作x2
n^2 [x^(1/n)-x^(1/n+1)]=[(n+1)/n][1/n-1/(n+1)]*[x^(1/n)-x^(1/n+1)]
[1/n-1/(n+1)]*[x^(1/n)-x^(1/n+1)]为a^x在0处的导数
即得答案是lnx