This worksheet illustrates Example 4.3 from the lecture notes: [math]\sum_{i=1}^n (2i{-}1) = n^2[/math].

[list=1] [*] Move the slider to vary [math]n[/math], and see what happens to the number of ([color=#006400]green[/color] and [color=#ff0000]red[/color]) dots. [*] Count the [color=#ff0000]red[/color] dots and convince yourself that there are [math]2n{-}1[/math] of them. [/list]