1. Use induction to prove that
The result is true for .
Suppose that and that the result holds for n:
I must prove it for . Using the induction hypothesis, I have
This proves the result for , so the result holds for all , by induction.
The Fibonacci numbers are defined by
2. Prove that
I'll use induction.
For , I have and . The result is true for .
Assume that the result is true for n:
This proves the result for , so the result is true for all by induction.
Real stories, in distinction from those we invent, have no author. - Hannah Arendt
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