[b]Example 11. The sum of the geometric series with first term a ratio of [math]\frac{1}{4}[/math].[/b][br]This applet is a construction based on the Rick Mabry's solution of the problem for finding the sum of the geometric series [math]S=\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^3}+\ldots [/math][br]See f.[2][br][br][url=https://tube.geogebra.org/m/38902][size=85]More details.[/size][/url]

[b]Example 12.  Golden Triangles and Infinite Series [/b][br]This example shows a way to evaluate the series:[br][math]S_1=1+\frac{1}{\phi^2}+\frac{1}{\phi^4}+\ldots[/math][br][math]S_2=\frac{1}{\phi}+\frac{1}{\phi^3}+\frac{1}{\phi^5}+\ldots[/math][br][math]S_3=1+\frac{1}{\phi}+\frac{1}{\phi^2}+\frac{1}{\phi^3}+\ldots[/math][br]See f.[5][br][br][url=https://tube.geogebra.org/m/102157][size=85]More details.[/size][/url]