在二项分布的教学中,笔者发现了一个求二项展开式中系数最大的项的简便方法,在这里介绍给大家,与各位共同分享.一般地,如果ζ~B(n,p),其中0p1.考察不等式P(ζ=k+1)P(ζ=k)≥1.若P(ζ=k+1)P(ζ=k)=Ck+1npk+1qn-k-1Cnkpkqn-k=n-kk+1·pq≥1,即(n-k)p≥q(k+1),所以k≤np-q=Eζ-q In the teaching of binomial distribution, the author found a simple method to find the item with the largest coefficient in the expansion, which is introduced to you here and shared with you. In general, if ζ ~ B (n, p), Where 0p1. Investigate the inequality P (ζ = k + 1) P (ζ = k) ≥ 1. If P (ζ = k + 1) P (ζ = k) = Ck + 1npk + 1qn-k- 1Cnkpkqn- k = n-kk + 1 · pq ≧ 1, that is, (nk) p ≧ q (k + 1), k ≦ np-q = Eζ-q