2005/1乘2+2005/2乘3+2005/3乘4+······+2005/2004乘2005
=2005×(1-1/2+1/2-1/3+1/3-1/4+……+1/2004-1/2005)
=2005×(1-1/2005)
=2005-1
=2004
2005/1乘2+2005/2乘3+2005/3乘4+······+2005/2004乘2005
=2005×(1-1/2+1/2-1/3+1/3-1/4+……+1/2004-1/2005)
=2005×(1-1/2005)
=2005-1
=2004