If I am asked to find the least upper bound of the set A={ 2n/n+1 for all n in natural numbers} and then prove that, can I do that by writing that as a sequence and showing that it converges to 2? In other words, I think that the LUB is 2. Can I show that the sequence <2n/n+1 for n inN> converges to 2 to show that the LUB is 2?

Thanks.