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数学归纳法是数学中一种重要的证题方法,是培养与发展学生逻辑思维能力的好题材。从教学的实践来看,学生在运用这一方法证明问题时,感到困难的往往是实现第二步“P(k)真→P(K+1)真”的证明。而第二步关键在于怎样合理的运用归纳假设。下面谈谈个人几点不成熟的做法。一、讲清从“P(k)到P(k+1)”表达式项(因式)数的变化运用数学归纳法证明恒等式(或不等式)时,
Mathematical induction is an important test method in mathematics. It is a good subject for cultivating and developing students’ logical thinking ability. Judging from the teaching practice, when students use this method to prove problems, they often find it hard to prove the second step “P(k) true → P(K+1) true”. The key to the second step is how to reasonably use the inductive hypothesis. Let’s talk about personal immature practices. First, explain the use of mathematical induction to prove identities (or inequalities) when the number of expressions (factors) of the expressions P(k) to P(k+1) is changed.