an=1+1/2 +1/3+...+1/(3n-1),共有3n-1项,于是a(n+1)共有 3(n+1)-1=3n+2项,即最后一项为1/(3n+2)所以 a(n+1)=1+1/2+1/3 +...+1/(3n-1) +1/3n +1/(3n+1) +1/(3n+2)从而 a(n+1) -an =1/3n +1/(3n+1) +1/(3n+2)...