Pascal's Triangle Worksheet

You may want to read Pascal's Triangle before doing this worksheet.

• Show that (nr) + (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.