# How do you use a graphing calculator to find the limit of the sequence a_n=n^2/(n+1)?

the limit of the sequence is ${\lim}_{n \rightarrow \infty} \left({n}^{2} / \left(n + 1\right)\right)$ or the value ${n}^{2} / \left(n + 1\right)$ as $n$ gets really large.
type the function $y = {n}^{2} / \left(n + 1\right)$ into your calculator (you can replace $n$ with $x$)
graph the function on a large window. if the graph approaches a y-value when $x$ is very large, that value is your limit. otherwise, the limit is $\infty$ or $- \infty$.
since this graph has a continuously increasing y-value for large x values, the limit of the sequence ${a}_{n} = {n}^{2} / \left(n + 1\right)$ is $\infty$.