n^2[a^(1/n)-a^1/(1+n)]求极限a大于0,n趋向于无穷

Question

n^2[a^(1/n)-a^1/(1+n)]求极限
a大于0,n趋向于无穷

Answer 1

原式=lim(n→∞)(a^(1/n)-a^(1/(1+n)))/(1/n-1/(1+n))*(1/n-1/(1+n))*n^2
=lim(n→∞)(a^(1/n)-a^(1/(1+n)))/(1/n-1/(1+n))*lim(n→∞)n/(1+n)
=[a^x]'|(x=0)*1
=lna