作业帮已知1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4.计算1/2+1/6+1/12+1/201/30+1/42+1/56+1/72+1/90=?
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/02 21:27:13
已知1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4.计算1/2+1/6+1/12+1/201/30+1/42+1/56+1/72+1/90=?
已知1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4.计算1/2+1/6+1/12+1/201/30+1/42+1/56+1/72+1/90=?
已知1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4.计算1/2+1/6+1/12+1/201/30+1/42+1/56+1/72+1/90=?
1/2+1/6+1/12+1/201/30+1/42+1/56+1/72+1/90
=1-1/2+1/2-1/3+1/3-1/4+.+1/8-1/9+1/9-1/10
=1-1/10
=9/10
等于十分之九。 把它拆开。
应该是这样的吧“1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=”
原式=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