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Math Help - analysis 1 question

  1. #1
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    Unhappy 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.
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: analysis 1 question

    yes if you can show it converges to 2.
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  3. #3
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    Re: analysis 1 question

    I'll see if I can do that. Thanks.
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  4. #4
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    Re: analysis 1 question

    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.
    Thanks from jakncoke
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