# Sequence Converging Proof

## Homework Statement

Prove that if the sequence {An} converges to A, then the sequence {|An|} converges to |A|. And is the converse true?

This is for my calculus class and it needs to be in proof format. Thank you!

## The Attempt at a Solution

I'm totally lost, I was going to use ||x| - |y|| less than/or equal to |x-Y| but I'm not really sure where to go from there and if that's even right.

Related Calculus and Beyond Homework Help News on Phys.org
Just insert this inequality into the formal epsilon definition of the limit and you're done.
For the converse, consider the sequence 1,-1,1,-1,...

Last edited:
So, find the limit of that inequality?

What is the epsilon definition of the limit of a sequence?

Reversed Triangle Inequality will work:

l l An l - l A l l ≤ l An -A l

*Use formal espilon definition

Last edited:
l An - A l ≤ l An l - l A l
Above used for proving the Forward Direction
I don't think that works, because epsilon is on the right hand side ... you really need the other inequality already given by Mush89.

I don't think that works, because epsilon is on the right hand side ... you really need the other inequality already given by Mush89.
Opps! My bad! I guess the second inequality i've mentioned will be enough ..