Question 21
Let $ABCD$ be a unit square. Let $Q_1$ be the midpoint of $\overline{CD}.$ For $i=1,$ $2,$ $\ldots,$ let $P_i$ be the intersection of $\overline{AQ_i}$ and $\overline{BD},$ and let $Q_{i+1}$ be the foot of the perpendicular from $P_i$ to $\overline{CD}.$ What is
$$
\sum_{i=1}^{\infty}\text{Area of }\triangle DQ_iP_i?
$$
$$
\sum_{i=1}^{\infty}\text{Area of }\triangle DQ_iP_i?
$$