MIT6_042JS10_lec30

MIT6_042JS10_lec30 - Mathematics for Computer Science MIT...

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‹#› Albert R Meyer, April 21, 2010 lec 11W.1 Mathematics for Computer Science MIT 6.042J/18.062J Binomial Theorem, Combinatorial Proof Albert R Meyer, April 21, 2010 lec 11W.2 Polynomials Express Choices & Outcomes Products of Sums = Sums of Products Albert R Meyer, April 21, 2010 expression for c k ? lec 11W.3 Albert R Meyer, April 21, 2010 lec 11W.5 multiplying gives 2 n product terms: 11 ! 1 + X11X ! X1 + 1XX ! 1X1 + ! + XX ! X a term corresponds to selecting 1 or X from each of the n factors n times expression for c k ? Albert R Meyer, April 21, 2010 lec 11W.6 the X k coeff, c k , is # terms with exactly k X ’s selected n times expression for c k ? Albert R Meyer, April 21, 2010 lec 11W.7 The Binomial Formula binomial coefficients binomial expression (( )) + +++++ ++ = Image by MIT OpenCourseWare.
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‹#› Albert R Meyer, April 21, 2010 lec 11W.8 The Binomial Formula Albert R Meyer, April 21, 2010 lec 11W.9 The Binomial Formula Albert R Meyer, April 21, 2010 lec 11W.17 What is the coefficient of in the expansion of (X 1 +X 2 3 +…+X k ) n ?
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MIT6_042JS10_lec30 - Mathematics for Computer Science MIT...

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