Problem

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2019 Shortlist LC3 day1 (logical reasoning)

Tags: geometry, Squares, square, areas



Consider the following sequence of squares (side $1$), in each step the central square is divided into equal parts and colored as shown in the figure: Square 1 Square 2 Square 3 Let $A_n$ with $n \in N$, $n> 1$ be the shaded area of square $n$, show that $A_n <\frac23$