1/1×2+1/2×3+1/3×4+.+1/98×99+1/99×100

来源：学生作业帮助网编辑：六六作业网时间：2024/12/23 06:29:40

1/1×2+1/2×3+1/3×4+.+1/98×99+1/99×1001/1×2+1/2×3+1/3×4+.+1/98×99+1/99×1001/1×2+1/2×3+1/3×4+.+1/98×99+

1/1×2+1/2×3+1/3×4+.+1/98×99+1/99×100
1/1×2+1/2×3+1/3×4+.+1/98×99+1/99×100

1/1×2+1/2×3+1/3×4+.+1/98×99+1/99×100
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)+...+(1/98-1/99)+(1/99-1/100)
=(1-1/100)
=99/100