1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90用简便方法计算

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90用简便方法计算
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
用简便方法计算

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90用简便方法计算
分析：
1/2可以写成1-1/2
1/6可以写成1/2-1/3
1/12可以写成1/3-1/4
所以这个算式就=1-1/2+1/2-1/3+1/+.+1/9-1/10
一直正负抵消 最后剩第一项 和最后一项
得1-1/10=9/10

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=(1-1/2)+(1/2-1/3)+(1/3-1/4).(1/9+1/10)
=1-1/2+1/2-1/3+1/3-1/4.1/9-1/10
=1-1/10
=9/10