很多资料上都有下面的问题:求证nn+1>(n+1)n(n∈N,n≥3).此题结构匀称,形式优美,是一经典名题,现从本题的证明来探讨含正整数n的不等式的常见证明方法.法1(构造函数)即证n1n>(n+1)1n+1,即证lnn/n>ln(n+1)/n+1.设f(x)=lnx/x(x≥3),则 A lot of information on the following questions: Prove nn + 1> (n +1) n (n ∈ N, n ≥ 3). This title structure is well-proportioned and beautiful in form, is a classic title, now from the proof of this question The general proof method of inequalities with positive integers n is as follows: Method 1 (constructor) shows that n1n> (n + 1) 1n + 1, that is, lnn / n> ln (n + 1) / n + (x) = lnx / x (x≥3), then