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我认为讲授“二项式系数的性质”一节中第二条性质这样处理可能较好一些;先用不等式的知识证明系数C_n~0、C_n~1、…、C_n~r、…、C_n~n的左半段严格递增,再用第一条性质即可比较自然地得出中间有一项最大或有两项相等而且最大的结论,具体作法如下: 证明 n为偶数,当r+1≤n/2时,系数的左半段递增,中间恰有一项最大。事实上,由r+1≤n/2,得n/(r+1)≥2,故 (C_n~(r+1))/(C_n~r)=(n+1)/(r+1)-1=n/(r+1)-1+1/(r+1) ≥2-1+1/(r+1)>1。
I think it might be better to deal with the second property in the section “Properties of Binomial Coefficients”; first use the knowledge of inequalities to prove the coefficients C_n~0, C_n~1,..., C_n~r,..., C_n~ The left half of n is strictly incremented, and then the first property can be used to naturally conclude that there is one of the largest or two equal and largest conclusions in the middle. The specific approach is as follows: Prove that n is an even number when r+1 ≤ n At /2, the left half of the coefficient is incremented and the middle one is the largest. In fact, from r+1 ≤ n/2, n/(r+1)≥2, so (C_n~r+1)/(C_n~r)=(n+1)/(r+1) )-1=n/(r+1)-1+1/(r+1) ≥2-1+1/(r+1)>1.