EBK DISCRETE MATHEMATICS: INTRODUCTION
11th Edition
ISBN: 9781133417071
Author: EPP
Publisher: CENGAGE LEARNING - CONSIGNMENT
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- The Fibonacci sequence fn=1,1,2,3,5,8,13,21,... is defined recursively by f1=1,f2=1,fn+2=fn+1+fn for n=1,2,3,... a. Prove f1+f2+...+fn=fn+21 for all positive integers n. b. Use complete induction to prove that fn2n for all positive integers n. c. Use complete induction to prove that fn is given by the explicit formula fn=(1+5)n(15)n2n5 (This equation is known as Binet's formula, named after the 19th-century French mathematician Jacques Binet.)arrow_forwardGiven the recursively defined sequence , and , use complete induction to prove that for all positive integers .arrow_forward
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