Solutions to this problem are due midnight, Sunday, March 14, 2010

### Problem:

We are given a number .

The sequence is defined by:

for

How does the value of for large , depend on ?

A website of computational mathematics problems for middle and high school students

Solutions to this problem are due midnight, Sunday, March 14, 2010

We are given a number .

The sequence is defined by:

for

How does the value of for large , depend on ?

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**Problem**:

The sequence of Fibonacci numbers is defined as follows:

for .

The ratio of successive Fibonacci numbers is .

How fast does the size of the difference decay as increases?

**Problem**:

For each positive integer set .

Provide computational evidence that, as increases without bound, either:

(a) *does not* approach a limiting value, or

(b) *does* approach a limiting value and say what is that value.