Evaluate
\[\prod_{n = 1}^{2004} \frac{n^2 + 2n - 1}{n^2 + n + \sqrt{2} - 2}.\]
Question:
Evaluate
\[\prod_{n = 1}^{2004} \frac{n^2 + 2n - 1}{n^2 + n + \sqrt{2} - 2}.\]
Answer:
Let's think step by step.

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2004 \sqrt{2} - 2003
Evaluate
\[\prod_{n = 1}^{2004} \frac{n^2 + 2n - 1}{n^2 + n + \sqrt{2} - 2}.\]
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