Grades 11-12 Video Solutions 2023-2023_11-12

Video Transcription

Video Summary

The problem involves a square with an area of 84 divided into smaller squares, repeatedly coloring the upper left square black as the lower right square is further divided infinitely. Initially, the large black square has an area of 21, and subsequent black squares form a geometric series with each being 1/4 of the previous term. The series has a first term of 21 and a common ratio of 1/4. To find the total black area, the formula for the sum of an infinite geometric series, \(a/(1-r)\), is used. Calculating, the total black area sums to 28.

Keywords

infinite geometric series

square division

black area calculation

geometric series sum

area of squares