用定积分表示极限lim(n-->∞)ln((1+1/n)(1+2/n)……(1+n/n))^(2/n)

n→∞lim ln((1+1/n)(1+2/n)……(1+n/n))^(2/n)=lim 2(1/n)[ln(1+1/n)+ln(1+2/n)+……+ln(1+n/n)]=2∫²₁lnxdx=2x(lnx-1)|²₁=4(ln2-1)-2(ln1-1)=4ln2-2