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数学归纳法是证明与正整数n有关的数学命题的一种重要方法,其证题程序是:①验证n取第一个值n_0时结论正确;②假设n=k(k∈N~*,n≥n_0)时结论正确,证明当n=k+1时结论也正确;如果①、②两个步骤都完成了,则可断定结论对n≥n_0的一切正整数都正确.一般地说,第一个步骤易验证,但是大多数的同学在第二步犯难,结合几个具体的例子谈谈如何突破这个难点.
Mathematical inductive method is an important method to prove the mathematical propositions related to positive integer n. The testimony program is as follows: (1) When verifying that n takes the first value n_0, the conclusion is correct; (2) Assuming that n = k (k∈N ~ *, n≥n_0), the conclusion is correct, and the conclusion is correct when n = k + 1. If both steps ① and ② are completed, it can be concluded that all the positive integers of the conclusion are correct for n≥n_0. Generally speaking, The first step is easy to verify, but most of the classmates make a fuss in the second step. Talk about how to break through this difficult point with a few concrete examples.