Let \(\left\{x_{n}ight\}_{n=1}^{\infty}\) and \(\left\{y_{n}ight\}_{n=1}^{\infty}\) be sequences of real numbers such that

\[\lim _{n ightarrow \infty}\left(x_{n}+y_{n}ight)=s\]

and

\[\lim _{n ightarrow \infty}\left(x_{n}-y_{n}ight)=d\]

Prove that

\[\lim _{n ightarrow \infty} x_{n} y_{n}=\frac{1}{4}\left(s^{2}-d^{2}ight) \text {. }\]