## Problem Statement

Calculate the limit of the numerical sequence:

$\lim _{n \rightarrow \infty} \frac{2-5+4-7+\ldots+2 n-(2 n+3)}{n+3}$
## Solution

$\lim _{n \rightarrow \infty} \frac{2-5+4-7+\ldots+2 n-(2 n+3)}{n+3}=$
$=\{2-5=4-7=\ldots=2 n-(2 n+3)=-3\}=$
$=\lim _{n \rightarrow \infty} \frac{-3 \cdot n}{n+3}=\lim _{n \rightarrow \infty} \frac{\frac{1}{n} \cdot(-3) \cdot n}{\frac{1}{n}(n+3)}=$
$=\lim _{n \rightarrow \infty} \frac{-3}{1+\frac{3}{n}}=\frac{-3}{1}=-3$

## Problem Kuznetsov Limits 6-19