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Solved: In Exercises 1922, prove the given property of the
Chapter 3, Problem 22(choose chapter or problem)
QUESTION:
Prove the given property of the Fibonacci numbers for all \(n \leq 1\). (Hint: The first principle of induction will work.)
\([F(1)]^{2}+[F(2)]^{2}+\cdots+[F(n)]^{2}=F(n) F(n+1)\)
Questions & Answers
QUESTION:
Prove the given property of the Fibonacci numbers for all \(n \leq 1\). (Hint: The first principle of induction will work.)
\([F(1)]^{2}+[F(2)]^{2}+\cdots+[F(n)]^{2}=F(n) F(n+1)\)
ANSWER:Step 1 of 3
The first principle of induction is defined as:
1. Prove the property for the base case is true.
2. Assume that the property is true for some positive integer. And prove it for .