What's the Maximum

Algebra Level 3

Let S be a sequence whose first few terms are as follows: \( \frac{1}{503} , \frac{4}{524} , \frac{9}{581} , \frac{16}{692}, \ldots, \frac{n^2}{500 + 3n^3 } , \ldots \)

The largest term of the sequence can be expressed as \( \frac{N}{M} \)

Find the value of \(M-N\).

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