计算1＼1×2+1＼2×3+1＼3×4+……+1＼49×50要简便计算,有过程更好,急用
来源：学生作业帮助网 编辑：六六作业网 时间：2024/12/26 14:11:57
计算1＼1×2+1＼2×3+1＼3×4+……+1＼49×50要简便计算,有过程更好,急用
计算1＼1×2+1＼2×3+1＼3×4+……+1＼49×50要简便计算,有过程更好,急用
计算1＼1×2+1＼2×3+1＼3×4+……+1＼49×50要简便计算,有过程更好,急用
1＼1×2+1＼2×3+1＼3×4+……+1＼49×50
=1-1/2+1/2-1/3+1/3-1/4+……+1/49-1/50
=1-1/50
=49/50
1＼1×2+1＼2×3+1＼3×4+……+1＼49×50
=1-1/2+1/2-1/3+1/3-1/4+……+1/49-1/50
=1-1/50
=49/50
49/50
1/1X2+1/2X3+1/3X4+....+1/49×50
=(1-1/2)+(1/2-1/3)+................+(1/49-1/50)
=1-1/50
=49/50
1/1X2+1/2X3+1/3X4+....+1/[n（n+1）]
=(1-1/2)+(1/2-1/3)+................+[(1/n/(n+1)...
全部展开
1/1X2+1/2X3+1/3X4+....+1/49×50
=(1-1/2)+(1/2-1/3)+................+(1/49-1/50)
=1-1/50
=49/50
1/1X2+1/2X3+1/3X4+....+1/[n（n+1）]
=(1-1/2)+(1/2-1/3)+................+[(1/n/(n+1)]
=1-1/(n+1)
=n/(n+1)
类似：1/[a*(a+n)]=(1/n)*[1/a-1/(a+n)]
例子：
1/56=1/(7*8)=1/7-1/8
1/12=1/(2*6)=(1/4)*[1/2-1/6]
....................
等等
这个式子是很有用的
以上希望对你有所帮助~
收起
1＼1×2+1＼2×3+1＼3×4+……+1＼49×50
=(1/1 - 1/2) + (1/2 - 1/3)+(1/3-1/4)...+(1/49 - 1/50)
=1- 1/2 + 1/2 - 1/3 + 1/3...+ 1/49 - 1/50
=1- 1/50
=49/50