Fibonacci Sequence denotes the term of the Fibonacci sequence discussed in Section . Use mathematical induction to prove the statement.
EXAMPLE The Fibonacci Sequence
Find the first terms of the sequence defined recursively by , , and .
denotes the term of the Fibonacci sequence.
The Fibonacci sequence is recursively defined by …
Suppose is a statement depending on every natural number and the following conditions are satisfied.
For every natural number , if is true then is true.
Then is true for all natural numbers .
Let denote the Fibonacci sequence .
Step Show that is true.
Substitute for , for , and for in equation .
Substitute for in equation .
This implies that is true
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