(For students who have studied calculus) a. Explain how

Chapter 9, Problem 9.272

(choose chapter or problem)

(For students who have studied calculus) a. Explain how the equation below follows from the binomial theorem: (1+x)n = nk=0 n kxk. b. Write the formula obtained by taking the derivative of both sides of the equation in part (a) with respect to x. c. Use the result of part (b) to derive the formulas below. (i) 2n1 = 1 n n 1+2n 2+3n 3++nn n(ii)nk=1kn k(1)k =0d. Expressnk=1kn k3k in closed form (without using a summation sign or ellipsis).

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