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