infinite-dimensional subspaces of $\ell^1$

Question

I have the following problem to be addressed.

Knowing that $l_1$ is the vector space formed by all the sequences $a_{n} = (a_0, a_1, a_2...)$ such that:

$$\sum_{k=1}^{\infty} |a_{n}| < \infty $$

Find three examples of infinite-dimensional subspaces of $\ell^1$. Do not use $\ell^1$ as example.

The main problem is that I am struggling to figure out which is the form of an infinite-dimensional subspace of $\ell^1$ and I have no clues.

Answer 1

How about the set of all sequences with first/second/third coordinates 0?