求证log(n)(n+1)>log(n+1)(n+2),其中n∈N,且n>1

问题描述:

求证log(n)(n+1)>log(n+1)(n+2),其中n∈N,且n>1
n和n+1都是底数

要证:log(n)(n+1)>log(n+1)(n+2),
即要证log(n+1)/logn>log(n+2)/log(n+1)(换底公式)
即要证log(n+1)log(n+1)>logNlog(n+2)
而由基本不等式
lognlog(n+2)