Determine whether the given sequence $\{a_n\}$ is convergent by deciding on monotonicity and boundness. Explain your answer.
$$\{a_n\}=\frac{n+1}{2n+1}$$
Determine whether the given sequence $\{a_n\}$ is convergent by deciding on monotonicity and boundness. Explain your answer.
$$\{a_n\}=\frac{n+1}{2n+1}$$