Sequences, Continued

Exercises

Write for-statements in m-files to solve following exercises. Use format long.

1. The recurrence equation
   
   
   has two fixpoints and .
   Write a for-statement to iterate the recurrence equation 10 times.
   What happens if you start with and respectively?
   What happens if you iterate 50 times? 100 times?
2. Write a recurrence equation for the continued fraction
   
   Hint: it is easier to write a recurrence equation for the continued fraction plus 1.
   
   1. Find the limit of the recurrence equation by iterating in Octave.
   2. Find the exact value of the continued fraction by first finding the fixpoints of the recurrence equation you used in a and then subtracting 1.