论文部分内容阅读
在线段AB上,先在A点标注0,在B点标注2002,这称为第一次操作;然后在AB中点为C处标注0+2002/2=1001,称为第二次操作;又分别在得到的线段AC、BC的中点D、E处标注对应线段两端所标注的数字和的一半,即0+1001/2与1001+2002/2,称为第三次操作;照此下去,经过11次操作之后,在线段AB上所有标注的数字和是多少? 首先,寻找标注数字的规律.为了寻找规律,设B点标注的数字为m,则:
On line AB, first mark 0 at point A, and mark 2002 at point B. This is called the first operation; then at the AB midpoint, point C is marked 0+2002/2=1001, which is called the second operation; In addition, the midpoints D and E of the obtained line segments AC and BC are marked with the half of the sum of the numbers marked at both ends of the corresponding line segments, that is, 0+1001/2 and 1001+2002/2, which are referred to as the third operation; Then, after 11 operations, what is the number of all the labels on line AB? First, look for the rule of labeling numbers. To find the law, set the number marked with B to m, then: