26a-Binomial-Coefficients

26a-Binomial-Coefficients - Binomial...

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Binomial Coefficients Discrete Mathematics
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Discrete Mathematics – Binomial Coefficients 26-2 Previous Lecture Combinations with repetitions C(n + r – 1,n – 1) Also recall that
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Discrete Mathematics – Binomial Coefficients 26-3 A Binomial A binomial is simply the sum of two terms, such as x + y We are to determine the expansion of Let us start with Every term in the expansion is obtained as the product of a term from the first binomial, a term from the second binomial, and a term from the third binomial Each of the terms xxy, xyx, and yxx is obtained by selecting y from one of the 3 binomials. Therefore, the coefficient 3 of is, actually, the number of 1-combinations from a set with 3 elements
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Discrete Mathematics – Binomial Coefficients 26-4 The Binomial Theorem Theorem . Let x and y be variables, and let n be a nonnegative integer. Then Proof. The terms in the product when it is expanded are of the form for j = 0,1,2,…, n.
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26a-Binomial-Coefficients - Binomial...

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