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# Limits convergence help watch

1. 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
2. (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 .

You might find it easiest to observe ; 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 ). Please read the Asking Questions Guidelines and in particular the section on Ambiguous Notation.
3. (Original post by DFranklin)
I'm assuming you mean .

You might find it easiest to observe ; 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 ). 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?
4. (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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