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**1. Homework Statement**

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. Homework 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.