1乘2分之2004+2乘3分之2004+3乘4分之2004+4乘5分之2004+.+2003乘2004分之2004等于?

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×(1-1/2004)
=2004×2003/2004
=2003