I want to find out if the following sequence is convergent:
$$
a\_1 = 3,\quad
a\_{n+1} = \frac{7 + 3 a\_n}{3 + a\_n}, \quad (n ≥ 1)
$$
I am new at university and it would be great if someone has got a tip for me how to deal with this. THX a lot.