2/3乘4乘5+2/4乘5乘6+2/5乘6乘7+2/6乘7乘8+2/7乘8乘9+2/8乘9乘10

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 15:50:50
2/3乘4乘5+2/4乘5乘6+2/5乘6乘7+2/6乘7乘8+2/7乘8乘9+2/8乘9乘10

2/3乘4乘5+2/4乘5乘6+2/5乘6乘7+2/6乘7乘8+2/7乘8乘9+2/8乘9乘10
2/3乘4乘5+2/4乘5乘6+2/5乘6乘7+2/6乘7乘8+2/7乘8乘9+2/8乘9乘10

2/3乘4乘5+2/4乘5乘6+2/5乘6乘7+2/6乘7乘8+2/7乘8乘9+2/8乘9乘10
2/3*4*5+2/4*5*6+2/5*6*7+...+2/8*9*10
=1/3*4-1/4*5+1/4*5-1/5*6+1/5*6-1/6*7+...+1/8*9-1/9*10
=1/3*4-1/9*10
=1/12-1/90
=13/180