二项式定理的推广及应用

The Extensions and Applications of the Binomial Theorem
Abstract：This paper first introduces the background and the applications of the binomial theorem, which are the basic nature and the combinatorial meaning of the binomial coefficient, the applications in resolving the coefficients of  of the polynomials and proving combinatorial identities. Secondly, this article describes the extensions of the binomial theorem which involves the polynomial theorem and its applications, the binomial inversion formula and its applications. This text emphatically introduces the application of the binomial theorem.
Key words: Binomial theorem. Combinatorial identities. The inversion formula

1.二项式定理的相关背景    3
2.二项式定理及其应用    4
2.1二项式定理    4
2.2二项式系数的基本性质    7
2.3二项式系数的组合意义及应用    10
2.4二项式定理在组合恒等式证明中的应用    13
3.二项式定理的推广    16
3.1多项式定理及其应用    16
3.2二项式反演公式及应用    18
4.总结    20

1
1   1
1   2   1
1   3   3   1
1   4   6   4   1
1    5   10  10  5   1
1   6    15  20  15  6   1
…………………………………………………………

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