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由归纳法得到的某些与自然数有关的数学命题,我们常常用下面的方法来证明它们的正确性:先证明当 n 取第一个值 n_0(如 n_0=1时,命题成立,然后假设当 n=k(k≥n_0),命题成立,证明n=k+1时命题也成立.就可以断定这个命题对于 n 取第一值及其后的所有的自然数也都成立.这种证明方法叫做数学归纳法.数学归纳法,是我们数学证题中的一种重要的证题工具.对于数学归纳法,学生往往难以理解它的实质,对它的证题步骤往往是在形式上有所了解,
Some of the mathematical propositions related to natural numbers obtained by inductive methods, we often use the following methods to prove their correctness: first prove that when n takes the first value n_0 (if n_0 = 1, the proposition is true, and then assume n=k(k≥n_0), the proposition is true, and the proposition that n=k+1 is true is established. It can be concluded that this proposition is also true for all values of n and the first number and all subsequent natural numbers. This method of proof is called Mathematical induction. Mathematical induction is an important test tool in our mathematics test. For mathematical induction, students often find it difficult to understand its essence. ,