1/1*2+1/2*3+1/3*4+…1/98*99+1/99*100如何解答?
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/08/19 08:20:33
1/1*2+1/2*3+1/3*4+…1/98*99+1/99*100如何解答?
![1/1*2+1/2*3+1/3*4+…1/98*99+1/99*100如何解答?](/uploads/image/z/8803864-64-4.jpg?t=1%2F1%2A2%2B1%2F2%2A3%2B1%2F3%2A4%2B%E2%80%A61%2F98%2A99%2B1%2F99%2A100%E5%A6%82%E4%BD%95%E8%A7%A3%E7%AD%94%3F)
1/1*2+1/2*3+1/3*4+…1/98*99+1/99*100
=1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100
=1-1/100
=99/100
=1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100
=1-1/100
=99/100