lim [1/(n+1)+1/(n+2)+.+1/(n+n)]
n→∞
=lim (1/n)[1/(1+1/n)+1/(1+2/n)+.+1/(1+/n)]
n→∞
=∫1/(1+x)dx (积分区间：0→1)
=ln|1+x| (0→1)
=ln2
lim [1/(n+1)+1/(n+2)+.+1/(n+n)]
n→∞
=lim (1/n)[1/(1+1/n)+1/(1+2/n)+.+1/(1+/n)]
n→∞
=∫1/(1+x)dx (积分区间：0→1)
=ln|1+x| (0→1)
=ln2