Answer
Converges to $\dfrac{2}{3}$
Work Step by Step
We are given the sequence $a_n=\dfrac{2n+1}{3n+2}$
We will apply the nth test to check whether the given series converges or diverges.
So, we have
$\lim\limits_{n \to \infty} \dfrac{2n+1}{3n+2}=\lim\limits_{n \to \infty} \dfrac{2+1/n}{3+2/n}=\dfrac{2+0}{3+0}=\dfrac{2}{3}$
This means that the given sequence converges to $\dfrac{2}{3}$.
