Let A B C D be a unit square. Let Q_{1} be the midpoint of \overline{C D}. For i=1,2, \ldots, let P_{i} be the intersection of \overline{A Q_{i}} and \overline{B D}, and let Q_{i+1} be the foot of the perpendicular from P_{i} to \overline{C D}. What is
\sum_{i=1}^{\infty} \text { Area of } \triangle D Q_{i} P_{i} ?
Answer Choices
A. \dfrac{1}{6}
B. \dfrac{1}{4}
C. \dfrac{1}{3}
D. \dfrac{1}{2}
E. 1