Question

A side of a square is 16 inches. The midpoints of its sides are joined to form an inscribed square. Another one is drawn in such a way that its vertices would lie also at the midpoints of the sides of the second square. This process is continued. Find the sum of the areas of these infinite squares.

Answer 1

this might be simpler to visualise if you first start with a square of side length x and then draw the first inner square using the rules above to get:

Now, can you tell me what the side length of the inner square (y) will be in terms of x?