1/6-1/15+1/12-1/35+1/20-1/63 简便方法计算.

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