概率论方法证明数学公式的若干实例

Probability Theory Method to Prove Some Examples of Mathematical Formula

本文主要通过举例说明利用概率论的方法来解决初等代数和数学分析中的一些问题:利用概率的性质和方差的非负性证明不等式,利用中心极限定律求极限,并阐明利用概率方法的关键是根据不同的数学问题建立相应的随机模型,然后利用相关定理证明,从中显示出概率方法在应用上的广泛性和优越性.

This paper mainly illustrates some problems of algebra and mathematical analysis by the use of probabilistic methods.For example,using the nature of the probability theory proofs inequality;using the central limit theorem proofs limit and the key to clarify the use of probability method is according to the mathematical problem to construct the corresponding probability model.The extension and superiority of probability methods in application are showed.