Which is larger?

Algebra Level 4

Which is larger

10092017 or 10101009×10081008? 1009 ^ { 2017} \quad \text{ or } \quad 1010 ^ { 1009 } \times 1008 ^ {1008} ?

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

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