In the 3x3 grid, 6/9 is shaded and in the 4x4 grid, 10/16 is shaded.
If a 20x20 grid was shaded in the same way, what fraction would be shaded?
By collecting data for the first few grids and choosing denominators carefully.
|Size of Grid||Fraction Shaded|
6/9 = 2/3 = 4/6
10/16 = 5/8
15/25 = 3/5 = 6/10
It can be seen that (n + 1)/2n is shaded.
So in a 20x20 grid, 21/40 is shaded.
Can you prove that (n + 1)/2n is shaded on an grid?
(Hint: 1 + 2 + 3 + ... + n = ½n(n + 1).)