巧算1/4+1/12+1/24+1/40+1/60+1/84+1/112

1/4+1/12+1/24+1/40+1/60+1/84+1/112
=1/4+1/2(1/6+1/12+1/20+1/30+1/42+1/56)
=1/4+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)
=1/4+1/2(1/2-1/8)
=1/4+1/4-1/16
=1/2-1/16
=7/16