A sequence is a function from integers $n = 1, 2, 3, \dots$ to real numbers $a_n$.
Visually, we can think of these as discrete points on a graph.
Try typing your own $a_n$ formula below (e.g., 1/n, (-1)^n/n, log(n)/n).
A sequence $\{a_n\}$ converges to $L$ if for every $\varepsilon > 0$, there exists an $N$ such that for all $n > N$, $|a_n - L| < \varepsilon$.
The shaded horizontal band shows the $\varepsilon$-neighborhood of the limit, and the vertical line marks where the definition is satisfied.
Does the sequence $a_n = (-1)^n/n$ converge?