1+1/1+2+1/1+2+3+……+1/1+2+3+……+2000
=2/1x2+2/2x3+2/3x4+……+2/2000x2001
=2×(1-1/2+1/2-1/3+1/3-1/4+……+1/2000-1/2001)
=2×(1-1/2001)
=2×2000/2001
=4000/2001
1+1/1+2+1/1+2+3+……+1/1+2+3+……+2000
=2/1x2+2/2x3+2/3x4+……+2/2000x2001
=2×(1-1/2+1/2-1/3+1/3-1/4+……+1/2000-1/2001)
=2×(1-1/2001)
=2×2000/2001
=4000/2001