Answer
Diverges
Work Step by Step
It is given a sequence $a_n=\frac{4n^2-3n}{2n+1}$.
Calculate the limit of the sequence:
$\lim\limits_{n \to \infty}a_n=\lim\limits_{n \to \infty}\frac{4n^2-3n}{2n+1}$
$=\lim\limits_{n \to \infty}\frac{2n(2n+1)-5n}{2n+1}$
$=\lim\limits_{n \to \infty}2n-\frac{5n}{2n+1}$
$=\lim\limits_{n \to \infty}2n-\frac{5}{2+1/n}$
$=\lim\limits_{n \to \infty}2n-\lim\limits_{n \to \infty}\frac{5}{2+1/n}$
$=\infty-\frac{5}{2+0}$
$=\infty$
Since the limit of the sequence is infinity, the sequence diverges.
