1. ## Converging Sequence Theorem

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!

2. Originally Posted by Mush89
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.
Then you need to write out a formal proof for yourself.
Here is what it will be based upon, $\left||x|-|y|\right|\le |x-y|$.

Show us what you come up with.

3. I was going to plug that inequality into the definition of a limit, but is that going in the wrong direction?

4. Originally Posted by Mush89
I was going to plug that inequality into the definition of a limit, but is that going in the wrong direction?
It absolutely does not.
The sequence $(a_n)$ converges. That is the one we have control over. We use it the get a handle on the sequence $\left|(a_n)\right|$