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Revising for an exam and I've come across a pretty basic problem.

Question: Prove that the supremum of the set A : { 3n / (5n+1) :n€N} is 3/5

My answer: So 3n / (5n+1) ≤ 3n / 5n = 3/5 so 3/5 is an upper bound.

Now, We claim that 3/5 is the least upper bound. Take β < 3/5 so now I need a positive integer n > .........This is bit I don't know how to do.... (how do I choose this part?)

I then know that you re-arrange n>........ to see that the β we chose earlier is: β < 3n / (5n+1) which is impossible, hence Sup(A) = 3/5

I hope you understand what I mean..

Regards as always

Tam

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# Basic problem with supremum question.

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