uragging statements from the left column to the right column

Last updated: 10/9/2023

uragging statements from the left column to the right column below give a proof by induction of the following statement For all n 1 4 7 10 3n 1 n 3n 5 2 The correct proof will use 8 of the statements below Statements to choose from Thus P k 1 is true Let P n be the statement 4 7 10 3n 1 4 7 10 3 k 1 1 k 3k 5 3 k 1 1 3k 5k 2 3k 5k So 3k 4 6k 8 2 2 3k 11k 8 2 k 1 3 k 1 5 2 Observe that 4 Therefore by the Principle of Mathematical Induction P n is true for all nz 1 n 3n 5 2 By the inductive hypothesis 4 7 10 3k 1 Note that 4 7 10 3 k 1 1 4 7 10 3k 1 3 k 1 1 k 3k 5 2 Now assume that P k is true for an arbitrary integer k 1 1 3 1 5 is true So the base case P 1 Your Proof Put chosen statements in order in this column and press the Submit Answers button