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Cauchy Sequences

  • #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


Homework Equations


None


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.
 

Answers and Replies

  • #2
36
0
can you use the theorem: every convergent sequence, is a cauchy sequence

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

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