A sequence (sn) is said to converge to the real number s provided that for each ε > 0 there exists a real number N such that for all n that are natural numbers, n > N implies that lsn - sl < ε. If (sn) converges to s, then s is called the limit of the sequence (sn). If a sequence does not converge to a real number, it is said to diverge.
Using only the above definition, prove that
lim (3n + 1)/(n + 2) = 3.