1/2-1/(2*3)-1/(3*4)-1/(4*5)-1/(5*6)
=1/2-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-(1/5-1/6)
=1/2-1/2+1/3-1/3+1/4-1/4+1/5-1/5+1/6
=1/6