[n^(1+1/n)]/n>=n^(1+1/n)/n=n^(1/n)[n^(1+1/n)]/n<=(n^(1+1/n)+1)/n=n^(1/n)+1/nlim(n→∞)n^(1/n)=lim(n→∞)e^(lnn/n)=lim(n→∞)e^((1/n)/1) （洛必达法则）=lim(n→∞)e^(1/n)=1同理lim(n→∞)n^(1/n)+1/n=1所以原式=1
