简便计算：1/14+1/24+1/36+1/48+1/60+1/72

题目

简便计算：1/14+1/24+1/36+1/48+1/60+1/72
我打错了，应是1/12+1/24+1/36+1/48+1/60+1/72

答案

1/12+1/24+1/36+1/48+1/60+1/72=（1-3-1/4）+（1/4-1/6）*1/2+1/36+（1/6-1/8）*1/2+1/60+（1/8-1/9）=（1/3-1/4+1/8-1/9）+【（1/4-1/6+1/6-1/8）*1/2】+1/36+1/60=7/72+1/16+1/36+1/60=（7/72+1/36）+1/16+1/60=1/...