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Homework: Section 13.4 Question 3, Instructor-c... HW Score: 28.79%, 1.73 of 6 points O Points: 0 of 1 Use the principle of mathematical induction to show that the given statement is true for all natural numbers n. 7+8+9+ ... +(n+6) = =n(n + 13) What is the first step in a mathematical induction proof? O A. Show that the statement is true for n = k + 1. O B. Show that the statement is true for n = 1. O C. Show that the statement is true for n = k. O D. Show that the statement is true for n = 0. Write the statement for n = 1. 7+8+9+ ... + (n+6) = _n(n+13) (1 +6) = =1(1+13) 0=0 (Simplify your answers.) Is the statement true? O Yes O No Ask my instructor Print Media Clear all DEC 5 WHomework: Section 13.4 Question 3, Instructor-c... HW Score: 28.79%, 1.73 of 6 points O Points: 0 of 1 Sa Use the principle of mathematical induction to show that the given statement is true for all natural numbers n. 7+8+9+ ...+(n+6) = =n(n+ 13) . . . . . What is the next step in the proof? O A. Show that if the statement is true for k + 1, then the statement is true for k. O B. Show that the statement is true for k + 1. O C. Show that the statement is true for k. O D. Show that if the statement is true for k, then the statement is also true for k + 1. Write the statement for k. 7+8+9+ ...+ = (Do not simplify.) What do we do with this statement? A. Assume this statement is true for some natural number k, and use it to show that the statement is also true for the next natural number k + 1. O B. Assume this statement is true for some natural numbers k and k + 1, and use it to show that the statement is also true for the next natural number k + 1. O C. Assume this statement is true for some natural number k and the expression, n(n + 13) is true, and use it to show that the statement is also true for the next natural number k + 1. O D. Assume this statement is true for some natural number k + 1, and use it to show that the statement is also true for the next natural number k. Now we show that if the statement is true for some natural number k, then it is true for k + 1. What is the left side of the equation when n is replaced by k + 1? Ask my instructor Print Media Clear all Check an DEC 5 .... A WHomework: Section 13.4 Question 3, Instructor-c... HW Score: 28.79%, 1.73 of 6 points O Points: 0 of 1 Save Use the principle of mathematical induction to show that the given statement is true for all natural numbers n. 7+8+9+ ...+ (n+6) = =n(n+ 13) Now we show that if the statement is true for some natural number k, then it is true for k + 1. What is the left side of the equation when n is replaced by k + 1? O A. 7+8+9+ ...+(k+6) OB. 7+8+9+ ... +[(k+1)+6] O c. 1 (k + 1)[(k +1)+13] OD. 1 SK(k +13) The left side contains an additional term that is not in the equation when n is replaced by k. Adding that new term to both sides of the equation for k gives which of the following? O A. 7 +8 +9 + ...+[(k+1)+6] = =k(k+13) O B. 7 +8+9+ ... + (k +6) + [(k + 1) +6] = _k(k + 13) + [(k+1)+6] O c. 7+8+9+ ... +(k+6) +[(k + 1) +6] =7 +8+9+ ... + [(k+ 1)+6] OD. 7 +8+9+ ... + (k+6) +[(k+ 1) + 6] = =(k+ 1)[(k+1)+13] Ask my instructor Print Media - Clear all Check ansv DEC 5 W= Homework: Section 13.4 Question 3, Instructor-c... HW Score: 28.79%, 1.73 of 6 points Points: 0 of 1 Save Use the principle of mathematical induction to show that the given statement is true for all natural numbers n. 7+8+9+ ...+(n+6) = =n(n+ 13) . . . . . O A. Simplify 7 + 8 +9 + ... + [(k +1) + 6]. O B. Solve 7 + 8 + 9 + ... + (k +6) + [(k + 1) + 6] = = (k + 1)[(k + 1) + 13] for k. O c. Simplify - k(k + 13) + [(k + 1) +6]. O D. The proof is complete. Simplify. 7 K(K + 13 ) + [ (k +1 ) + 6] =[ (Type your answer in factored form.) Compare this statement to the original statement. Is this statement equal to the original statement with n = k + 1? O No O Yes Have we proven by the principle of mathematical induction that 7 + 8 + 9 + ... + (n + 6) = =n(n + 13)? Ask my instructor Print Media - Clear all Check answ DEC 5 W