Math 310-01/02

10-13-2017

1. Use induction to prove that

For ,

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:

Then

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*

Copyright 2017 by Bruce Ikenaga