## Problem Statement

Calculate the limit of the numerical sequence:

$$
\lim _{n \rightarrow \infty} \frac{(n+2)^{2}-(n-2)^{2}}{(n+3)^{2}}
$$
## Solution

$$
\begin{aligned}
& \lim _{n \rightarrow \infty} \frac{(n+2)^{2}-(n-2)^{2}}{(n+3)^{2}}=\lim _{n \rightarrow \infty} \frac{n^{2}+4 n+4-n^{2}+4 n-4}{n^{2}+6 n+9}= \\
& =\lim _{n \rightarrow \infty} \frac{\frac{1}{n} 8 n}{\frac{1}{n}\left(n^{2}+6 n+9\right)}=\lim _{n \rightarrow \infty} \frac{8}{n+6+\frac{9}{n}}=\left\{\frac{8}{\infty}\right\}=0
\end{aligned}
$$

## Problem Kuznetsov Limits 3-30