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可视化(或数形结合)方法证明不等式是一种创新,是我们解题教学追求的目标.可视化(或数形结合)方法解题往往构思巧妙,方法简洁,出奇制胜.本文旨在说明,我们在解题中充分应用这种思想方法,培养学生的数学素质,对提高解题能力,发展思维会有很大的帮助.例1(2001年全国卷II,理20)已知m,n∈N+,且m(1+n)m.证明:原不等式等价于nln(1+m)>mln(1+n),
Visualization (or combination of number and form) proves that inequality is a kind of innovation, which is the goal of our solution to the problem of teaching pursuit.Visualization (or the combination of number and shape) method is often conceived in a clever way, with concise method and surprisingly winning.This paper aims to show that we The full application of this method of thinking and solving problems, to develop the mathematical quality of students, to improve the ability to solve problems, the development of thinking will be a great help Example 1 (2001 Volume II, Li 20) known m, n ∈ N + (1 + m) n> (1 + n) m. Proof: The original inequality is equivalent to nln (1 + m)> mln (1 + n)