计算:2005×(1/1×2+1/2×3+1/3×4+…+1/2003×2004+1/2004×2005)

问题描述:

计算:2005×(1/1×2+1/2×3+1/3×4+…+1/2003×2004+1/2004×2005)

2005×(1/1×2+1/2×3+1/3×4+…+1/2003×2004+1/2004×2005)
=2005×(1-1/2+1/2-1/3+1/3-1/4+…+1/2003-1/2004+1/2004-1/2005)
=2005×(1-1/2005)
=2005×2004/2005
=2004

2005×(1/1×2+1/2×3+1/3×4+…+1/2003×2004+1/2004×2005)
=2005×[(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2004-1/2005)]
=2005×(1-1/2005)
=2005-1
=2004