# Cauchy Sequences

1. Mar 18, 2008

### ricardianequiva

1. The problem statement, all variables and given/known data
Prove that the following sequence is Cauchy:
a_n = [a_(n-1) + a_(n-2)]/2 (i.e. the average of the last two), where
a_0 = x
a_1 = y

2. Relevant equations
None

3. The attempt at a solution
I was trying to use the definition of Cauchy (i.e. |a_m - a_n| < e) by relating a_n - a_(n-1) to a_(n-1) - a_(n-2), but to no avail.

2. Mar 19, 2008

### b0it0i

can you use the theorem: every convergent sequence, is a cauchy sequence

just prove the sequence converges, cite the theorem, and you're finished