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Using the Negated definition of convergence watch

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    Any help with this question? I've got an answer to the proceeding question, but I need some guidance using the definition
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    (Original post by thomoski2)
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    Any help with this question? I've got an answer to the proceeding question, but I need some guidance using the definition
    Mind sharing the preceding question, if it relates to part b?
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    (Original post by RichE)
    Mind sharing the preceding question, if it relates to part b?
    Part a is just the negated definition of convergence
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    So, if you look at your definition, the first thing you're going to need to do is pick an epsilon that "doesn't work". That is \epsilon > 0 such that however large N is, we can find n > N with |a_n - 3| > \epsilon.

    So, what might be a good choice for epsilon?

    Hint: if you're not sure, one thing to do is see if you can see what a_n does converge to - this will give you an idea of "how close to 3" epsilon needs to be. (e.g. if a_n converged to 10, then since |10 - 3| = 7, any epsilon < 7 is likely to work. Although I would actually then choose epsilon = 1 just for ease of subsequent calculations).
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    (Original post by thomoski2)
    Part a is just the negated definition of convergence
    So the first quantifier says there is an epsilon.... what epsilon have you chosen?
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    (Original post by DFranklin)
    So, if you look at your definition, the first thing you're going to need to do is pick an epsilon that "doesn't work". That is \epsilon &gt; 0 such that however large N is, we can find n > N with |a_n - 3| &gt; \epsilon.

    So, what might be a good choice for epsilon?

    Hint: if you're not sure, one thing to do is see if you can see what a_n does converge to - this will give you an idea of "how close to 3" epsilon needs to be. (e.g. if a_n converged to 10, then since |10 - 3| = 7, any epsilon < 7 is likely to work. Although I would actually then choose epsilon = 1 just for ease of subsequent calculations).
    I tried finding what it converged to but I tried up to n=10 and it seemed to converge to 3 so I don't know what epsilon to use
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    (Original post by Bobby21231)
    I tried finding what it converged to but I tried up to n=10 and it seemed to converge to 3 so I don't know what epsilon to use
    It certainly doesn't converge to 3!
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    (Original post by DFranklin)
    It certainly doesn't converge to 3!
    Oops I just realised I used (7n/n+2)-3 which explains why I was confused
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    (Original post by DFranklin)
    It certainly doesn't converge to 3!
    I got it converged to 7 so mod 7-3 =4 so epsilon<4
 
 
 
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