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  3. point y dragging statements from the left column t

point y dragging statements from the left column to the right column below give a...

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Basic Math

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point y dragging statements from the left column to the right column below give a proof by induction of the following statement For all n 1 we have 1 1 2 3 5 8 Fn Fn 2 1 where Fr is the nth Fibonacci number F 1 F 1 and Fn Fn 1 Fn 2 he correct proof will use 8 of the statements below Statements to choose from Your Proof Put chosen statements in order in this column and press the Submit Answers button Let P n be the statement 1 1 2 3 Fn Fn 2 1 That is assume 1 1 2 3 Fk Fk 2 1 For the base case note that P 1 is true becuase F 1 2 1 F3 1 Now assume that P k is true for an integer k 1 Then adding Fl 1 to both sides of this equation we get 1 1 2 3 Fe F 1 Fk 1 Fk 2 1 Using the recursive formaul for Fibonacci numbers this simplifies to 1 1 2 3 Fe 1 Fk 3 1 Therefore P k 1 is true Therefore by the Principle of Mathematical Induction P is true for all m

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