1/30+1/42+1/56+1/72+1/90+1/100+1/110+1/132

来源：百度知道编辑：UC知道时间：2024/05/27 02:56:46

如题,
不知道有没有简便方法吗?

1/30=1/5-1/6
1/42=1/6-1/7
1/56=1/7-1/8
……
1/100=1/10-1/11
1/132=1/11-1/12
1/30+1/42+1/56+1/72+1/90+1/100+1/110+1/132
=1/5-1/6+1/6-1/7+1/7-1/8+……+1/10-1/11+1/11-1/12
=1/5-1/12
=7/60

1/30=1/5-1/6,1/42=1/6-1/7以此类推得答案为1/5-1/12=7/60

我只给你提点。
1/30=1/(5*6)=1/5-1/6
1/42=1/(6*7)=1/6-1/7
我想剩下的不难了。

1/30+1/42+1/72+1/90+…1/9900 巧算 1/30+1/42+1/56+1/72+1/90 1/2+1/6+1/12+1/20+1/30 30/1+42/1+56/1+72/1+90/1=? 1/12+1/20+1/30+1/42+1/56=?? 1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90= 1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=? 1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30=? 计算1/2 +1/6+1/12+1/20+1/30+1/42= 求解1/2-1/6-1/12-1/20-1/30-1/42