2/2*3 +2/3*4 +2/4*5 +.2/19*20
来源：学生作业帮助网 编辑：六六作业网 时间：2024/11/22 17:37:38
2/2*3+2/3*4+2/4*5+.2/19*202/2*3+2/3*4+2/4*5+.2/19*202/2*3+2/3*4+2/4*5+.2/19*202/2*3+2/3*4+2/4*5+.2/1
2/2*3 +2/3*4 +2/4*5 +.2/19*20
2/2*3 +2/3*4 +2/4*5 +.2/19*20
2/2*3 +2/3*4 +2/4*5 +.2/19*20
2/2*3 +2/3*4 +2/4*5 +.2/19*20
=2*（1/2*3 +1/3*4 +1/4*5 +.1/19*20）
=2*[(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+.+(1/19-1/20)]
=2*[1/2-1/3+1/3-1/4+1/4-1/5+.+1/19-1/20]
=2*[1/2-1/20]
=2*9/20
=9/40
2/2×3 +2/3×4 +2/4×5 +......2/19×20
=2×(1/2×3 +1/3×4 +1/4×5 +......1/19×20)
=2×[(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+......+(1/19-1/20)]
=2×[1/2-1/3+1/3-1/4+1/4-1/5+......+1/19-1/20]
=2×(1/2-1/20)
=2*9/20
=9/10