數學歸納法Mathematical Induction是數學上的一種證明方法, 其被用於證明某個給定公式或 定理 在整個自然數範圍內成立且不須知道推導公式或定理 卻能證明公式或定理是否正確的方法. 換言之,其為證明函數ƒ(x)的公式是否成立的方法  - 先證起始點是正確, 如命起始點n=1時而ƒ(1) 成立, 並設n=k時ƒ (k) 成立且n=k+1時也成立. 所以此函數公式是成立的.此觀念與骨牌遊戲的原理是一樣. 如n=1成立推至n=k=1 n=k+1=2也成立,現在n=k=2成立推至n=k+1=3也成立,於至列推n=k=任何都成立. 以下是用數學歸納法證明ån2 = n(n+1)(2n+1)/6 是否正確,與用數學歸納法推導及證明隸美佛定理的例子. Mathematical inductionis a method of mathematical proof that a given formula or theory, whether is true for all natural numbers or not with and without knowing how to derive the formula or theory. It is done by proving that the initial point a formula or theory is true, and then proving that if any one point in the formula is true, then the next one is true, too. For example, let n=1 is true then n=k=1 Þ n=k+1=2 is true.  Since n = 2 is true, then n=k+1=2 Þ n=k+1=3 is also true. By doing so, n= k = any number can be proven to be true.  The following are two examples to demonstrate how to use Mathematical induction to prove that ån2 = n(n+1)(2n+1)/6 is true, even one does not know how to derive the formula and also to derive and prove De Moivre's Theorm.

 

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