数学不仅是一门演绎的科学,同时也是实验的科学,数学中的许多结论是通过观察、实验、归纳、猜想等合情推理方式得到的.近年来中考和数学竞赛中常以这种题材来考查学生数学探索能力和创新能力.下面举例说明.例1　直线上有n个点,我们进行如下的操作:每相邻两点间插入1个点,经过3 Mathematics is not only a deductive science but also an experimental science. Many conclusions in mathematics are obtained through observation, experimentation, induction, and conjecture, etc. In recent years, examinations and mathematical competitions often use this subject matter to examine. Students’ ability to explore mathematics and their ability to innovate are illustrated below. Example 1 There are n points on the line. We perform the following operations: Insert 1 point between each two adjacent points, passing 3