1*2分之1+2*3分之1+3*4分之1...2004*2005分之1=?

用裂项法：
1/(1*2)+1/(2*3)+1/(3*4)+……+1/(2004*2005)
= (1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2004-1/2005)
= 1-1/2005
= 2004/2005