Powers of 2 in plain sight

Number Theory Level pending

Let α \alpha be the value of the sum:

i = 1 2013 ( ( 1 ) n + 1 × 2 n ) \sum _{ i=1 }^{ 2013 }{ { ((-1) }^{ n+1 } } \times { 2 }^{ n })

Find the last three digits of α \alpha


The answer is 662.

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