x(x+3)分之1+(x+3)(x+6)分之1+(x+6)(x+9)分之1+(x+6)(x+9)分之1+...+(x+9

x(x+3)分之1+(x+3)(x+6)分之1+(x+6)(x+9)分之1+(x+6)(x+9)分之1+。。。+(x+99)(x+102)分之1=1/3 [x(x+3)分之3+(x+3)(x+6)分之3+(x+6)(x+9)分之3+(x+6)(x+9)分之3+。。。+(x+99)(x+102)分之3]=1/3[1/x-1/(x+3)+1/(x+3)-1/(x+6)+1/(x+6)-1/(x+9)+……+1/(x+99)-1/(x+102)]=1/3[1/x-1/(x+102)]=1/3×102/x(x+102)=34/(x²+102x)看其中的一个3/(x+3)(x+6)=[(x+6)-(x+3)]/(x+3)(x+6)=(x+6)/(x+3)(x+6)-(x+3)/(x+3)(x+6) =1/(x+3)-1/(x+6)这个方法称为裂顶法