Suppose that $(c_{j, n})$ is a real infinite dimensional triangular array where $1 \leq j \leq n$ with the properties that $\max\limits_{1 \leq j \leq n } |c_{j, n}| \rightarrow 0$ and $\sum\limits_{j=1}^n c_{j, n} \rightarrow \lambda$ when $n\rightarrow\infty$, and $\sup\limits_{n\in\mathbb{N}} \sum_{j=1}^n |c_{j, n}|<\infty.$
Please help me to prove that therefore $\prod\limits_{j=1}^n(1+c_{j, n})\rightarrow e^\lambda$.