29-33 ■ Fibonacci Sequence denotes the nth term of the Fibonacci sequence discussed in Section . Use mathematical induction to prove the statement.
For all ,
For all , by mathematical induction
denote the nth 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 2 for in equation
This implies that is true.
Step Assume that is true.
Step Show that it is true for
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