·一道高中不等式证明题请写出详细点的证明过程谢谢~\(≥▽≤)/~
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·一道高中不等式证明题请写出详细点的证明过程谢谢~\(≥▽≤)/~
题在图上
![](http://img.wesiedu.com/upload/7/00/700021018ed00cff4550ff71bbc4e666.jpg)
题在图上
![](http://img.wesiedu.com/upload/7/00/700021018ed00cff4550ff71bbc4e666.jpg)
![·一道高中不等式证明题请写出详细点的证明过程谢谢~\(≥▽≤)/~](/uploads/image/z/1358321-41-1.jpg?t=%C2%B7%E4%B8%80%E9%81%93%E9%AB%98%E4%B8%AD%E4%B8%8D%E7%AD%89%E5%BC%8F%E8%AF%81%E6%98%8E%E9%A2%98%E8%AF%B7%E5%86%99%E5%87%BA%E8%AF%A6%E7%BB%86%E7%82%B9%E7%9A%84%E8%AF%81%E6%98%8E%E8%BF%87%E7%A8%8B%E8%B0%A2%E8%B0%A2%7E%5C%28%E2%89%A5%E2%96%BD%E2%89%A4%29%2F%7E)
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
=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