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ing statements from the left column to the right column below give a proof by...

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Basic Math

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ing statements from the left column to the right column below give a proof by induction of the following statement ect proof will use 8 of the statements below Statements to choose from Let an be a sequence such that ap 0 and for all integers k 1 a 8a 1 3 Then for all integers n 0 1 8n 1 8 Your Proof Put chosen statements in order in this column and press the Submit Answers button Note that your proof should only contain of the statements on the left 1 gn Let P n be the statement an 3 1 8 Now assume that P k is true for an arbitrary integer k 0 This simplifies to 1 8 1 8 ak 1 3 8 a 3 3 3 8 8k 1 8 8 8 1 1 1 8 3 3 1 8811 0 Note that 1 80 1 1 3 3 1 8 1 8 1 8 as required for the truth of the base case 1 8 By the recurrence relation we have ak 1 8ax 3 8 3 1 3 Thus P k 1 is true Then a Therefore by the Principle of Mathematical Induction P n is true for all n 1 a 3

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