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    Hi,

    I'm struggling with proving that a sequence converges.

    as lim>infinity (6/n+4) - (3/n-2)=0

    I have been able to do similar questions but when i get 3n-24/n^2+2n-8 i get confused.

    Any help is appreciated.
    li
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    (Original post by Ttrx)
    Hi,

    I'm struggling with proving that a sequence converges.

    as lim>infinity (6/n+4) - (3/n-2)=0

    I have been able to do similar questions but when i get 3n-24/n^2+2n-8 i get confused.

    Any help is appreciated.
    li
    I'm assuming you mean \lim_{n \to \infty} \dfrac{6}{n+4} - \dfrac{3}{n-2}.

    You might find it easiest to observe - \dfrac{3}{n-2} <  \dfrac{6}{n+4} - \dfrac{3}{n-2} <  \dfrac{6}{n+4}; I'm assuming you can show both single fractions tend to 0, and you can then apply a squeeze theorem.

    As a side note, "(6/n+4) - (3/n-2)" is malformed (or at least, does not mean what you think it does, the strictly correct interpretation is (\frac{6}{n}+4) - (\frac{3}{n}-2)). Please read the Asking Questions Guidelines and in particular the section on Ambiguous Notation.
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    (Original post by DFranklin)
    I'm assuming you mean \lim_{n \to \infty} \dfrac{6}{n+4} - \dfrac{3}{n-2}.

    You might find it easiest to observe - \dfrac{3}{n-2} <  \dfrac{6}{n+4} - \dfrac{3}{n-2} <  \dfrac{6}{n+4}; I'm assuming you can show both single fractions tend to 0, and you can then apply a squeeze theorem.

    As a side note, "(6/n+4) - (3/n-2)" is malformed (or at least, does not mean what you think it does, the strictly correct interpretation is (\frac{6}{n}+4) - (\frac{3}{n}-2)). Please read the Asking Questions Guidelines and in particular the section on Ambiguous Notation.
    Would it be possible to do the question without applying a squeeze theorem or is that the only way to go?
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    (Original post by Ttrx)
    Would it be possible to do the question without applying a squeeze theorem or is that the only way to go?
    No, it's not the only way to go. It is the method I'd recommend, though.

    Edit: alternatively, replace the numerator/denominator of the fraction you've found by appropriate estimates to find an appropriate choice of N for given epsilon.
 
 
 
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