1 point Below are the steps of a proof by induction that 2n

Last updated: 10/9/2023

1 point Below are the steps of a proof by induction that 2n 1 2 for all integers n 3 Arrange the given steps in the correct order 2k 1 2 2k 2 by inductive hypothesis By the principle of mathematical induction we conclude that the statement is true for all integers n 3 Assume that 2k 1 2k for some integer k 3 2 k 1 1 2k 1 2 by algebra The statement is true for n 3 because 2 3 1 7 8 2 2k 2 2k 2k because k 3 v 2k 2k 2 2k 2k 1 by algebra Therefore 2 k 1 1 2k 1 which shows the statement is true for k 1