1/1×2+1/2×3+1/3×4+.+1/9×10=

来源：学生作业帮助网编辑：六六作业网时间：2024/08/11 15:43:23

1/1×2+1/2×3+1/3×4+.+1/9×10=1/1×2+1/2×3+1/3×4+.+1/9×10=1/1×2+1/2×3+1/3×4+.+1/9×10==1/1-1/2+1/2-1/3+1/

1/1×2+1/2×3+1/3×4+.+1/9×10=
1/1×2+1/2×3+1/3×4+.+1/9×10=

1/1×2+1/2×3+1/3×4+.+1/9×10=
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1-1/10
=9/10