1. Give an algebraic proof of Vandermonde's Identity k m (+) = () () k i=0...

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1. Give an algebraic proof of Vandermonde's Identity k m ("+") = (") (²) k i=0 Hint: Calculate the coefficient of rk in (1+x)m+n in two different ways. You will need the fact that if you have two polynomials p(x) = ao + a₁x + a₂x² + then the coefficient of ek in the product p(x)q(x) is ++amx and g(x) = bo + b₁x + b₂x² + ... + bnx Σa;bk-i- i=0 1. Give an algebraic proof of Vandermonde's Identity k m ("+") = (") (²) k i=0 Hint: Calculate the coefficient of rk in (1+x)m+n in two different ways. You will need the fact that if you have two polynomials p(x) = ao + a₁x + a₂x² + then the coefficient of ek in the product p(x)q(x) is ++amx and g(x) = bo + b₁x + b₂x² + ... + bnx Σa;bk-i- i=0

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Let us consider Binomial expansion of 1xm mn mith m x KO ... View the full answer