先求n^(1/n)的极限记n=x,求lim[x→+∞] x^(1/x)=lim[x→+∞] e^[(1/x)lnx]=lim[x→+∞] e^[(lnx/x)]=e^0=1由于n^(1/n)极限为1,你问的(1/n)^(1/n)是它的倒数,当然极限也为1补充：lim[x→+∞] lnx/x的极限用一次洛必达...