Dear Colleagues,

Could you please help me in solving the following problem:

If $\displaystyle (x_{n})$ is a Cauchy sequence in the metric space $\displaystyle (X,d)$ and $\displaystyle (y_{n})$ in $\displaystyle X$ such that $\displaystyle d((x_{n}),(y_{n}) \longrightarrow 0 $as $\displaystyle n\longrightarrow \infty$then show that$\displaystyle (y_{n})$ is Cauchy in $\displaystyle X $.