Suppose that n is a positive integer.Arrange the steps in the correct order to show that 2 divides n² + n using mathematical induction.Rank the options below.As the sum of two multiples of 2 is again a multiple of 2, 2 divides (k+ 1)² + (k+ 1).(k+ 1)² + (k+ 1) = (k² + 2k + 1) + (k + 1) = (k² + k) + 2(k+1)The inductive hypothesis is that 2 divides k² + k.12+1=2 and 212, so the basis step is clear.2 divides k² + k by inductive hypothesis, and clearly 2 divides 2(k + 1).▶

Answered: Image /qna-images/answer/dbc8ed1e-75b2-4727-be72-3295ff11eedf.jpg

Suppose that n is a positive integer. Arrange the steps in the correct order to show that 2 divides n²+ n using mathematical induction. Rank the options below. As the sum of two multiples of 2 is again a multiple of 2, 2 divides (k+ 1)2 + (k+1). (k+ 1)2 + (k+1)= (k² + 2k + 1) + (k+ 1) = (k² + k) + 2(k+1) The inductive hypothesis is that 2 divides k² + k. 12+1=2 and 212, so the basis step is clear. 2 divides K² + k by inductive hypothesis, and clearly 2 divides 2(k+ 1). V

Suppose that n is a positive integer. Arrange the steps in the correct order to show that 2 divides n²+ n using mathematical induction. Rank the options below. As the sum of two multiples of 2 is again a multiple of 2, 2 divides (k+ 1)2 + (k+1). (k+ 1)2 + (k+1)= (k² + 2k + 1) + (k+ 1) = (k² + k) + 2(k+1) The inductive hypothesis is that 2 divides k² + k. 12+1=2 and 212, so the basis step is clear. 2 divides K² + k by inductive hypothesis, and clearly 2 divides 2(k+ 1). V

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.5: Mathematical Induction

Problem 42E

See similar textbooks

Similar questions

Show that if the statement is assumed to be true for , then it can be proved to be true for . Is the statement true for all positive integers ? Why?
Use mathematical induction to prove the formula for all integers n_1. 5+10+15+....+5n=5n(n+1)2
Find (nk1)+(nk) and write the answer as a binomial coefficient in the form (nk) . Prove it. Hint:Use the fact that, for any integer p, such that p1 , p!=p(p1)! .
Prove by induction that n2n.