Edit made on January 03, 2015 by ColinWright at 18:38:50
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The binomial theorem tells us that the expansion of EQN:(x+y)^n is given by:
EQN:c_0x^n+c_1x^{n-1}y+c_2x^{n-2}y^2+...+c_ny^n |>> $c_0x^n+c_1x^{n-1}y+c_2x^{n-2}y^2+...+c_ny^n$ <<|
where the EQN:c_i are the binomial coefficients.
Writing the expansion using the binomial coefficients we get:
|>>
${n\choose~0}x^n+{n\choose~1}x^{n-1}y+{n\choose~2}x^{n-2}y^2+{n\choose~3}x^{n-3}y^3+\ldots+{n\choose~n}y^n$
<<|
The coefficients are exactly the numbers in the appropriate row of Pascal's Triangle.