19.1.2.4 Convergence in metric spaces

Problem: Does the sequence of elements converge on the space \( l_{1} \) ? \[ x_{n}=\left(\frac{1-n^{2}}{n^{2}}, \frac{2-n^{2}}{n^{2}}, \ldots, \frac{n-n^{2}}{n^{2}}, 0,0, \ldots, 0, \ldots\right) \text {. } \]