By dragging statements from the left column to the right column below give a proof by induction of the following statement For

Question

By dragging statements from the left column to the right column below give a proof by induction of the following statement For all n 1 1 22 n n n 1 2n 1 6 The correct proof will use 8 of the statements below Note that 1 Statements to choose from 1 1 1 2 1 1 6 Now assume that P k is true for an arbitrary integer k 1 1 2 P 1 is true Let P n be the statement 1 2 k 1 k k 1 2k 1 6 So the base case n n 1 2n 1 6 Then we see that k 1 k k 1 2k 1 6 k 1 6 6 2k 3k k 6k 12k 6 6 6 2k 9k 13k 6 6 k 1 k 2 2k 3 Then 12 22 k 6 k 1 k 1 1 2 k 1 1 Note that 12 22 k 1 2 12 2 k k 1 k k 1 2k 1 6 Therefore by the Principle of Mathematical Induction P n is true for all n 1 Thus P k 1 is true Your Proof Put chosen statements in order in this column and press the Submit Answers button

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