1/2-1/6-1/12-1/20-1/30-1/42
=1/2-(1/6+1/12+1/20+1/30+1/42)
=1/2-[1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)]
=1/2-(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7)
=1/2-(1/2-1/7)
=1/2-1/2+1/7
=1/7