Let { a n } be a geometric progression with a 1 = 2 and common ratio − 2 1 . For all n ∈ N , let us define two sets of coordinates P n and Q n as follows: P n = ( n , a n ) , Q n = ( n , 0 ) . What is the value of n = 1 ∑ 2 0 A n when A n is the area of the triangle P n Q n Q n + 1 ?
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