Pascal's Triangle: Difference between revisions
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[[File:Pascaltriangle.svg|thumb|Pascal's Triangle]] | [[File:Pascaltriangle.svg|thumb|Pascal's Triangle]] | ||
The coefficients of binomial expansion can be easily seen from the Pascal triangle. | The coefficients of binomial expansion can be easily seen from the Pascal triangle. The number is a sum of the two numbers above it. | ||
=== Pascal's triangle: Negative 1 === | |||
This can be extended to negative numbers easily. | |||
Revision as of 19:34, 19 October 2022
Introduction
Binomial expansion
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} (a+b)^0 &= 1 \\ (a+b)^1 &= a + b \\ (a+b)^2 &= a^2 + 2ab + b^2 \\ (a+b)^3 &= (a+b)(a+b)^2=(a+b)(a^2 + 2ab + b^2) \\ &= a^3 + 2a^2 b + ab^2 +ba^2 + 2ab^2+b^3 \\ &= a^3 + 3a^2 b + 3ab^2+b^3 \\ (a+b)^4 &= \cdots \end{align} }
Pascal's triangle
The coefficients of binomial expansion can be easily seen from the Pascal triangle. The number is a sum of the two numbers above it.
Pascal's triangle: Negative 1
This can be extended to negative numbers easily.
