Thread: subtraction series from each other

I am working on cauchy criterion and I am trying to show that a series converges to a limit. After showing basic proofs, i am trying to relate this to my case.

Now is the following that I have done correct?

Thanks for any help,

ps. Apologies for the infractions.

You have not provided enough information for someone to begin to help you.
It is always best to post the complete question exactly as written.

Sorry.

I have attached my question below. I am trying to show the convergence and giving Cauchy's Convergence Criterion. So I have defined Sn and Sm as you can see in the original attachment.

Part of the process is to take both sequences away from each other within the modulos. I am wondering if I have managed to take both sequences away from each other successfully.

Thanks