Metric Space (Elementary Analysis)

Metric Space (Elementary Analysis)

Let $X \subseteq \mathbb{R}^{n}$ be given by
$$ X = \left\{ (b_{1}, \ldots, b_{n}) \in \mathbb{R}^{n} \mid
\sum\limits_{i=1}^{n} \frac{b_{i}}{i} = 0 \right\}$$
Then prove that $X$ is closed in $\mathbb{R}^{n}$.