You may want to read Pascal's Triangle before doing this worksheet.
- Show that
(nr − 1) =
(n + 1r) by:
- Analogy with Pascal's triangle.
- Definition of the combination operation.
- Expand (x + y)8.
For each of the numbers in the first
eight rows of Pascal's Triangle, find
the remainder when that number is
divided by 2, and colour all
corresponding blocks for numbers that
have a remainder of 1. You may colour the triangle on the right.
- Visit the web site http://mathlair.allfunandgames.ca/pascal.php
and observe the patterns produced by a few different moduli.
Comment on the types of patterns obtained.