So I have an infinite sequence: $u = (u_1, u_2, u_3, . . .)$, where $u_j$ are real numbers. $l_1, l_2, l_\infty$ is defined as
$$||u||_1=\sum_{j\in \mathbb{N}} |u_j|$$ $$||u||_2=\sqrt{\sum_{j\in\mathbb{N}}|u_j|^2}$$
$$||u||_\infty=\sup_{j\in \mathbb{N}} |u_j|$$
I want to find an example such that $||u||_2 < \infty$, but $||u||_1$ is infinite. I have thought of examples between $||u||_1, ||u||_2$ and $||u||_\infty$, but I'm stuck on this one between $||u||_1$ and $||u||_2$