Give example of congregate serieses in the metric space : $(R^n,d_1),d_1=\sum_{i=1}^{n}\mid x_i-y_i \mid$

Question

Give example of congregate serieses in the metric space : $$(R^n,d_1),d_1=\sum_{i=1}^{n}\mid x_i-y_i \mid$$

What I tried:

I think I should find $\{X_n\}\to x$

$\left(\frac{\sin n}{n},\left(1+1/n\right)^n\right)\xrightarrow{n\to \infty}\left(0,e\right)$

How shoould I approach this type of questions?

Answer 1

Let $\{a_m\}_{m}\subset \mathbb R$ be a sequence such that $\sum_ma_m$ is absolutely convergence to $a$ and consider $\{(a_m,a_m,...,a_m)\}_m\subset \mathbb R^n$ which is convergence by $d_1$ to $na$