Let \(\left\{\left\{X_{n, k}ight\}_{k=1}^{n}ight\}_{n=1}^{\infty}\) be a triangular array of random variables where \(X_{n, k}\) has a \(\operatorname{BERnOulli}\left(\theta_{n, k}ight)\) distribution where \(\left\{\left\{\theta_{n, k}ight\}_{k=1}^{n}ight\}_{n=1}^{\infty}\) is a triangular array of real numbers that are between zero and one. Find a non-trivial triangular array \(\left\{\left\{\theta_{n, k}ight\}_{k=1}^{n}ight\}_{n=1}^{\infty}\) such that the assumptions of Theorem 6.2 hold and describe the resulting conclusion for the weak convergence of

\[\sum_{k=1}^{n} X_{n k}\]