证明{xn}单调有界即可
对于单调性
x(n+1)-xn=1/(2n+1)+1/(2n+2)-1/(n+1)=1/[(2n+1)(2n+2)]>0,{xn}单增
对于{xn}有界,下界显然xn>0
而上界xn=1/(n+1)+1/(n+2)+...+1/(n+n)