CALCULUS W/SAPLING ACCESS >IC<
4th Edition
ISBN: 9781319323394
Author: Rogawski
Publisher: MAC HIGHER
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Chapter C, Problem 6E
To determine
To prove:
usingthe principle of mathematical induction.
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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_forwardConsider the sequence defined by an=68n. Is an=421 a term in the sequence? Verify the result.arrow_forward
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