# Application of Geometric Progression

Algebra Level pending

Let $$\{a_n\}$$ be a geometric progression with $$a_1=2$$ and common ratio $$-\frac{1}{2}.$$ For all $$n\in \mathbb{N}$$, 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 $$\displaystyle \sum_{n=1}^{20}A_n$$ when $$A_n$$ is the area of the triangle $$P_nQ_nQ_{n+1}?$$

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