Proof by Induction Use mathematical induction to show that the given statement is true.
Formula for a Recursive Sequence A sequence is defined recursively by and . Show that for all natural numbers .
The statement for all natural numbers for the sequence defined recursively as .
The sequence is given as,
Prove basic step for . Assume the statement is true for some natural number and show that the statement is true for .
Denote the statement “ for all natural numbers for the sequence defined recursively as ” by .
This proves Step .
Assume is true for some . This is called the induction hypothesis
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