## Problem Statement

Calculate the limit of the numerical sequence:

$\lim _{n \rightarrow \infty} \frac{(n+1)^{3}-(n-1)^{3}}{(n+1)^{2}-(n-1)^{2}}$
## Solution

$\lim _{n \rightarrow \infty} \frac{(n+1)^{3}-(n-1)^{3}}{(n+1)^{2}-(n-1)^{2}}=\lim _{n \rightarrow \infty} \frac{n^{3}+3 n^{2}+3 n+1-n^{3}+3 n^{2}-3 n+1}{n^{2}+2 n+1-n^{2}+2 n-1}=$

$=\lim _{n \rightarrow \infty} \frac{6 n^{2}+2}{4 n}=\lim _{n \rightarrow \infty}\left(\frac{3}{2} n+\frac{1}{2 n}\right)=+\infty$

## Problem Kuznetsov Limits 3-25