·一道高中不等式证明题请写出详细点的证明过程谢谢~\(≥▽≤)/~

logn(n+1)-log(n-1) n
=lg(n+1)/lgn-lgn/lg(n-1)
=[lg(n+1)lg(n-1)-(lgn)^2]/lgnlg(n-1)
n>2
lg(n+1)>lg(n-1)>0
lg(n+1)lg(n-1)
≤[(lg(n+1)+lg(n-1))]^2 /4
=[lg(n+1)(n-1)]^2 /4
=[lg(n^2-1)]^2 /4