- #1

Enjoicube

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## Homework Statement

assuming an and bn are cauchy, use a triangle inequality argument to show that cn=

| an-bn| is cauchy

## Homework Equations

an is cauchy iff for all e>0, there is some natural N, m,n>=N-->|an-am|<e

## The Attempt at a Solution

I am currently trying to work backwards on this one, since we know

for some m,n>=N where N is a natural

2e>|-an+am|+|bn-bm|

Thus, through the triangle inequality this is >=|am-an+bn-bm|=|(bn-an)-(bm-am)|>=|bn-an|-|bm-am|.

Am I going completely wrong somewhere, because I am getting very stuck here. To anyone who answers, please only hints, not full answers (I am sure this is customary). Again, many thanks.