lim1/n+1/(n+1)+......1/2n=?

n趋近没穷大

lim1/n+1/(n+1)+......1/2n=lim{(1/n)*(1/(1+0/n)+1/(1+1/n)+1/(1+2/n)+……+1/(1+n/n))}=函数1/(1+x)在区间[0，1]上的定积分=ln(1+1)-ln(1+0)=ln2