答：
1/6+1/12+1/20+1/30+1/42+1/56
=1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1/2-1/8
=3/8