 # (For students who have studied calculus.) Explain how the equation below follows from the binomial theorem: ( 1 + x ) n = ∑ k = 0 n ( n k ) x k . Write the formula obtained by taking thederivative of both sides of the equationin part (a) with respect to x . Use the result of part (b) to derivative the formulas below. (i) 2 n − 1 = 1 n [ ( n 1 ) + 2 ( n 2 ) + 3 ( n 3 ) + ⋅ ⋅ ⋅ + n ( n n ) ] (ii) ∑ k = 0 n k ( n k ) ( − 1 ) k = 0 Express ∑ k = 1 n k ( n k ) 3 k in closed form (without using a summation sign or ellipsis). ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193 ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193

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Chapter 9.7, Problem 55ES
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