Question 161
Let $T$ be a triangle with area $1$. We let $T_{1}$ be the medial triangle of $T$, i.e. the triangle whose vertices are the midpoints of sides of $T$. We then let $T_{2}$ be the medial triangle of $T_{1}$, $T_{3}$ the medial triangle of $T_{2}$, and so on. What is the sum of the areas of $T_{1}, T_{2}, T_{3}, T_{4}, \ldots$?