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From the Fun Fact files, here is a Fun Fact at the Easy level:

Pascal's Triangle

Figure 1
Figure 1

Consider the triangle in Figure 1, called Pascal's triangle. It consists of numbers where each entry is the sum of the two entries above it.

Do you recognize the numbers in each row? This a quick way to generate the coefficients of (x+y)n from algebra!

And, better yet, you can use them as a quick way to calculate the powers of 11, since 11=10+1. Notice that 11, 121, 1331, and 14641 are all powers of 11...

Presentation Suggestions:
Draw several rows. Ask what 114 and 115 are! As a challenge, 116 is harder; you have to carry...

The Math Behind the Fact:
The generation of Pascal's triangle works because in long multiplication of a polynomial by (x+y), you end up adding adjacent coefficients of the polynomial together. The Fun Fact Multiplication By 11 is based on this idea.

How to Cite this Page:
Su, Francis E., et al. "Pascal's Triangle." Math Fun Facts. <http://www.math.hmc.edu/funfacts>.

Keywords:    combinatorics, binomial coefficients
Subjects:    algebra, combinatorics, number theory
Level:    Easy
Fun Fact suggested by:   Francis Su
Suggestions? Use this form.
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