运用柯西不等式证明：4/7

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