Divergent or convergent?

Question

If $$A_n = \frac{n(n+3)}{(n+1)^2}$$ then is the sum of the sequence $\sum(A_n)$ convergent or divergent?

Answer 1

Hint: In order for $\sum A_n$ to be convergent, it is required that $A_n \to 0$ as $n \to \infty$.

Answer 2

HINT:

The terms of the series tend to $1$.

Answer 3

HINT: $\lim A_n=1$ and the limit for convergent series is...