Some help with the following would be great.
Let $(X,||\cdot||)$ be a normed space.
Let $(x_{n})_{n}$ and $(y_{n})_{n}$ be Cauchy sequences in $(X, D)$. Say also that $s_{n} = ||x_{n} + y_{n}||$.
Prove that $s_{n}$ is a Cauchy sequence in $(\mathbb{R}, |\cdot|)$.
Use the following:
$\large{|} \hspace{2pt} \normalsize||x-y||-||u-v|| \hspace{2pt}\large{|} \normalsize \le ||x-u|| + ||y-v||$
So I'm guessing we need to use the fact that $(x_{n})_{n}$ and $(y_{n})_{n}$ are Cauchy, then need to get it into the form of the hint.
But how?