To solve this problem, we need to find a common denominator for all the fractions in the numerator and denominator.

Numerator:
1/2 + 1/3 + 1/4 + ... + 1/2000
= (1000/2000) + (1333/2000) + (1500/2000) + ... + (1/2000)
= (1000 + 1333 + 1500 + ... + 1) / 2000
= (1 + 2 + 3 + ... + 1999) / 2000

Denominator:
1999/1 + 1998/1 + 1997/1 + ... + 1/1999
= (1999 + 1998 + 1997 + ... + 1) / 1
= (1 + 2 + 3 + ... + 1999) / 1

Therefore, the expression simplifies to:
(1 + 2 + 3 + ... + 1999) / 2000
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(1 + 2 + 3 + ... + 1999) / 1

Since the numerator and denominator are the same, the expression simplifies to 1.