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O A. No, since we have only shown that Sk+ 1 satisfies the statement. OB. No, since we must show that S, satisfies the statement. OC. Yes.

O A. No, since we have only shown that Sk+ 1 satisfies the statement. OB. No, since we must show that S, satisfies the statement. OC. Yes.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please, if possible, circle the answer so that I can understand the steps. Please write clearly if you write by hand so that I can read the numbers. I appreciate your understanding.
This question has three parts, and here is the third part, and I will send you the second and third parts separately

To continue the proof by induction, begin with 1•13 +2•14+3 • 15 + ... + k(k + 12) = A. n(n+12) B. k(k+12) C. k(k-12) D. (k+ 1)(k+13) Add this term to both sides of the equation. 1.13+2 14+3•15+ ...+k(k+12) 1.13+2 14+ 3 • 15 + ... + k(k + 12) + = = k(k+ 1)(2k +37) 6 k(k+ 1)(2k + 37) 6 (Type your answer in factored form.) Simplify the right side. Factor the numerator. 1.13+2 14+3•15+ ... + k(k + 12) + (k + 1)(k+ 13) = + k(k+ 1)(2k +37) 6 O A. No, since we have only shown that Sk + 1 satisfies the statement. B. No, since we must show that S₁ satisfies the statement. C. Yes. D. No, since we must show that S₁ + 1 satisfies the statement. which is assumed to be true, and add the k + 1 term to both sides of the formula. What is this term? (Type your answer in factored form.) The right side of the above equation is Sk + 1. Have we finished proving the given statement for all positive integers n?
Transcribed Image Text:To continue the proof by induction, begin with 1•13 +2•14+3 • 15 + ... + k(k + 12) = A. n(n+12) B. k(k+12) C. k(k-12) D. (k+ 1)(k+13) Add this term to both sides of the equation. 1.13+2 14+3•15+ ...+k(k+12) 1.13+2 14+ 3 • 15 + ... + k(k + 12) + = = k(k+ 1)(2k +37) 6 k(k+ 1)(2k + 37) 6 (Type your answer in factored form.) Simplify the right side. Factor the numerator. 1.13+2 14+3•15+ ... + k(k + 12) + (k + 1)(k+ 13) = + k(k+ 1)(2k +37) 6 O A. No, since we have only shown that Sk + 1 satisfies the statement. B. No, since we must show that S₁ satisfies the statement. C. Yes. D. No, since we must show that S₁ + 1 satisfies the statement. which is assumed to be true, and add the k + 1 term to both sides of the formula. What is this term? (Type your answer in factored form.) The right side of the above equation is Sk + 1. Have we finished proving the given statement for all positive integers n?
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