Math 310-01/02

10-13-2017

1. Use induction to prove that

For ,

The result holds for .

Assume that and that the result holds for n:

I must prove the result for . Using the induction hypothesis, I have

This proves the result for . Hence, the result is true for all , by induction.

2. A sequence of integers is defined by

Prove that for ,

For ,

For ,

Assume the result is true for all . In particular, it is true for and for . So

This proves the result for n. Hence, the result is true for all by induction.

*Our experience is composed rather of illusions lost than of
wisdom acquired.* - *Joseph Roux*

Copyright 2017 by Bruce Ikenaga