证明：先证明左边,利用柯西不等式
（1/(n+1)+1/(n+2)+...+1/2n)(n+1+n+2+...2n)>=(1+1...+1)^2=n^2
=>（1/(n+1)+1/(n+2)+...+1/2n)>=n^2/((3n+1)2n/2)=2n/(3n+1)=2/(3/2+1/n)
显然在n=2时2/(3/2+1/n)取最小值,故2n/(3n+1)>=4/7
当且仅当1/（n+1)=1/(n+2)...1/2n且n=2取等号,显然是取不到的,故有
4/7