二项式定理的应用是高三复习中一类难度较大的问题 .经常碰到学生问及诸如 (52 +7) 2ｎ+ 1的整数部分的整除性或小数部分的估计等问题 .通过对(Ａ +Ｂ) ｎ 展开式的分析 ,我们得到如下结论 .定理 1　设ｎ ,Ａ ,Ｂ∈Ｎ ,且Ｂ - 1Ａ Ｂ +1,记Ｉ为 (Ａ +Ｂ) ｎ 的整数部分 ,Ｆ为 The application of the binomial theorem is one of the more difficult problems in the third year review. Frequently, the student asks questions such as the divisibility of the integral part of (52 +7) 2n+ 1 or the estimation of the fractional part. A +B) n expansion analysis, we get the following conclusions. Theorem 1 Let n, A, B∈N, and B - 1A B +1, note that I is the integer part of (A + B) n, F is