## Problem Statement

Calculate the limit of the numerical sequence:

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

$$
\begin{aligned}
& \lim _{n \rightarrow \infty} \frac{(2 n+1)!+(2 n+2)!}{(2 n+3)!}=\lim _{n \rightarrow \infty}\left(\frac{(2 n+1)!}{(2 n+3)!}+\frac{(2 n+2)!}{(2 n+3)!}\right)= \\
& =\lim _{n \rightarrow \infty}\left(\frac{1}{(2 n+2)(2 n+3)}+\frac{1}{2 n+3}\right)=0+0=0
\end{aligned}
$$

## Problem Kuznetsov Limits 6-2