2004/(1×2)+2004/(2×3)+2004/(3×4)+2004/(4×5)+……+2004/(2003×2004)=2004×[1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+……+1/(2003×2004)]=2004×(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……1/2003-1/2004)=2004×(1-...那2乘5分之3+5乘8分之3+8乘11分之3+.....+1997乘2000分之3+2000乘2003分之3等于？？你好：同学3/(2×5)+3/(5×8)+3/(8×11)+……+3/(1997×2000)+3/(2000×2003)=1/2-1/5+1/5-1/8+1/8-1/11+……+1/1997-1/2000+1/2000-1/2003=1/2-1/2003=2001/4006