现行中学数学教材中涉及到这样一类无穷数列: 若α为无理数,将α依次精确到个位,十分位,百分位,千分位,……的不足(或过剩)近似值所构成的数列. 例如,按以上精确度依次取π的不足近似值所得的无穷数列为 3,3.1,3.14,3.141,3.1415,…… 在教学中,我们常听有些教师称这样的数列不存在通项公式.有的数学书刊也以上述数列作为找不出通项公式的数列的示例. 这里,我们仅用大家熟知的函数{X}(表示 The current mathematics textbook for middle schools involves such an infinite number of columns: If α is an irrational number, α is successively refined to a sequence of one, tenth, hundredth, thousandth,... Inferior (or surplus) approximations. For example, the infinities obtained by taking the inadequacy of π in order of the above precision are 3, 3.1, 3.14, 3.141, 3.1415,... In teaching, we often hear some teachers saying that such a series does not have a general term formula. Mathematical books and magazines also use the above series as an example of a series that cannot find a general formula. Here, we only use the well-known function {X} (indicating