A sequence (sn) is said toconvergeto the real numbersprovided that for eachε> 0 there exists a real numberNsuch that for allnthat are natural numbers,n>Nimplies that lsn- sl <ε.If (sn) converges tos, thensis called thelimitof the sequence (sn). If a sequence does not converge to a real number, it is said todiverge.

Using only the above definition, prove that

lim (3n+ 1)/(n +2) = 3.