Is the sequence $\{\frac{1}{n}e_n\}_{n \in \mathbb{N}}$ a Schauder basis of $\ell^2$ over $\mathbb{C}$

Question

Let $\{e_n\}_{n \in \mathbb{N}}$ be the standard basis of $\ell^2$ over $\mathbb{C}$

Let $\{b_n\}_{n \in \mathbb{N}}$ be the sequence such that $\forall n \in \mathbb{N}: b_n = \frac{1}{n}e_n$

My question is if $\{b_n\}_{n \in \mathbb{N}}$ is a Schauder basis of $\ell^2$ over $\mathbb{C}$

Thanks.