1. Give an algebraic proof of Vandermonde's Identity k m ("+") = (") () 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 + ax + ax + then the coefficient of ek in the product p(x)q(x) is ++amx and g(x) = bo + bx + bx + ... + bnx a;bk-i- i=0