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Essay / Research Paper Abstract
This 4 page paper provides an overview of the central elements of Pascal's triangle. Bibliography lists 4 sources
Page Count:
4 pages (~225 words per page)
File: MH11_MHPasca2.rtf
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Unformatted sample text from the term paper:
is an example of Pascals Triangle: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1
1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126
84 36 9 1 (Katsiavriades, 2003). This triangle represents an equation that is continuous, that repeats and that is predictable. Essentially, each number on the
triangle is the sum of the two numbers above it (Katsiavriades, 2003). For example, the 8 on line 9 is the sum of the 1 and 7 in line
8. The next line in Pascals Triangle, if it were to continue from the example given, would be: 1, 10 (1 + 9), 45 (9
+ 36), 120 (36 + 84), etc. (Katsiavriades, 2003). Pascals Triangle is based on the algebraic principles of binomial expansion. This is based on the principle that
expanded expressions are defined by a distinct pattern and that understanding the formulas for these patterns creates the predictability of the patterned outcomes. One formula for binomial expansion, for
example, is the following: (1 + x)2 This formula can also be expressed as the following: (1 + x)(1 + x) or 1 + 2x + x2 (Katsiavriades, 2003).
This same process can also be cubed, for example, (1+x)3, and the following
ways of expressing the formula help us better understand Pascals Triangle: (1 + x)3 = (1 + x)(1 + x)(1 + x) = (1 + x)(1 + 2x + x2)
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