Otro
Infinite number of squares inside a square
Autor
Kabai, Sándor
Resumen
Series, Calculus and Analytic Geometry A series of squares are aligned along the diagonal of a unit square. Each square has edge length half the size of the previous square and is attached to the previous square at a corner. The sum of the areas of this series of squares is ¼+1/16+...+1/(2^2n). As n tends to infinity the sum converges to 1/3, as three such series fill the unit square. This is one way to see that the sum of the infinite series 1/(2^2n) is 1/3 Componente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemática