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The limits on an as n goes to infinity is a

Then for some epsilon greater than 0, chose N such that for n>N

we have |an-a| < epsilon.

Now if m and n are > N we have |an-am|=|(am -a)-(an -a)|

< or= |am -an | which is < or equal to 2 epsilor so the sequence is Cauchy.

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Q: Prove that every convergent sequence is a Cauchy sequence?
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