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在解决比较复杂的问题时,可以先分析这个问题的几个简单、特殊的情况,从中发现、归纳出规律,从而找到解决问题的方法。这种研究问题的方法叫作“经验归纳法”。【例1】自1开始,每隔两个整数写出一个整数,得到一列数:1,4,7,10……第100个数是几?【解】根据已知条件,直接写出100个数太麻烦了,但写出前几个数还是比较容易的:4=1+3×1,7=4+3=1+3×2,10=7+3=1+3×3
When solving more complicated problems, we can analyze a few simple and special cases of this problem, discover and summarize the law, and find the solution to the problem. This method of studying the problem is called “empirical induction.” [Example 1] Starting from 1, every two integers to write an integer, get a number: 1,4,7,10 ...... The number of the first 100? [Solution] According to the known conditions, directly write 100 The number is too much trouble, but it is easy to write the first few numbers: 4 = 1 + 3 × 1, 7 = 4 + 3 = 1 + 3 × 2, 10 = 7 + 3 = 1 + 3 × 3