Friday Puzzle

(First, I'm still interested in further responses to the prior post if any care to contribute...)

But on to a Friday puzzle I've adapted from the same essential problem recently presented over at CTK Insights:

What is the final answer for this computation:

3/2 x 4/3 x 5/4 x 6/5 x…. x 1999/1998 x 2000/1999 = ______

Answer below:
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ANSWER: 1000

Peruse the first 3 possible results…

3/2 x 4/3 = 12/6 = 2/1 or 4/2

3/2 x 4/3 x 5/4 = 60/24 = 5/2

3/2 x 4/3 x 5/4 x 6/5 = 360/120 = 3/1 or 6/2

...it becomes clear that the answer always entails the final given numerator over the initial denominator or "2".
Thus, the answer for the problem as stated is 2000/2 or 1000.