1/6-1/15+1/12-1/35+1/20-1/63
=1/6+1/12+1/20-(1/15+1/35+1/63)
=1/2*3+1/3*4+1/4*5-(1/3*5+1/5*7+1/7*9)
=1/2-1/3+1/3-1/4+1/4-1/5-1/2(1/3-1/5+1/5-1/7+1/7-1/9)
=1/2-1/5-1/2(1/3-1/9)
=1/2(1-1/3+1/9)-1/5
=1/2×7/9-1/5
=7/18-1/5
=35/90-18/90
=17/90