证明：ln(n+1)-ln(n)=ln((n+1)/n)=ln(1+1/n)1/1+1/2+1/3...+1/n>ln(2)-ln(1)+ln(3)-ln(2)...+ln(n+1)-ln(n)
=ln(n+1)-ln(1)=ln(n+1)
故原命题得证