Thread: analysis 1 question

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 in N> converges to 2 to show that the LUB is 2?

Thanks.

yes if you can show it converges to 2.

I'll see if I can do that. Thanks.

Yes, but you need in addition that the sequence {2n/(n+1)} is increasing. Example {1+1/n} has limit 1 but the least upper bound is 2.