Let $P_{0},P_{1},P_{2},\cdots,P_{n}$ be $n+1$ points in the plane. Let $ d=1$ denote the minimal value of all the distances between any two points. Prove that
$$\dfrac{1}{P_{0}P_{1}}+\dfrac{1}{P_{0}P_{2}}+\cdots+\dfrac{1}{P_{0}P_{n}}<\sqrt{15n}$$
This problem background is from China high school math competition (Oct 14, 2012) problem 15,can see http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2822547&sid=bbbc81f99da00d657f61b4835931c87e#p2822547
also can see this two solution:http://wenku.baidu.com/view/82fb84d4240c844769eaeea3.html
But for my problem,I can't prove it.and I think this is nice problem,and Thank you for your help.