Which is larger?

Algebra Level pending

Which is larger

\[ 1008 ^ { 2017} \quad \text{ or } \quad 1009 ^ { 1009 } \times 1007 ^ {1008} ? \]

Hint: \( a_n = \left( 1 + \dfrac{1}{n} \right)^{n+1} \) for \( n = 1, 2, 3, \ldots \) is a decreasing sequence.

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