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Exploring Pascal's Triangle

Advanced Level

Working with a partner, study the following array of numbers. What patterns do you see in the arrangement of the numbers? Describe each pattern using words and symbols.

 

As you look for patterns, try to answer the following questions:

1. Can you predict the next row of numbers?
2. Is there a pattern in the sums of the numbers in the rows?
3. Do any numbers repeat?
4. Can you find a pattern in the diagonal numbers?

Share your discoveries with the group.

See if you can find:

natural numbers          1, 2, 3, 4, ...	pentatope numbers        1, 5, 15, 35, 70, ...
powers of 2          2, 4, 8, 16, ...	Catalan numbers        1, 2, 5, 14, 42, ...
powers of 11         11, 121, 1331, 14641, ...	Fibonacci numbers        1, 1, 2, 3, 5, 8, ...
triangular numbers          1, 3, 6, 10, ...	binomial coefficients
tetrahedral numbers          1, 4, 10, 20, ...	probability & combinations
hexagonal numbers          1, 6, 15, 28, ...	Sierpinski triangle

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