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# Using the Negated definition of convergence watch

1. Any help with this question? I've got an answer to the proceeding question, but I need some guidance using the definition
2. (Original post by thomoski2)

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?
3. (Original post by RichE)
Mind sharing the preceding question, if it relates to part b?
Part a is just the negated definition of convergence
4. 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 such that however large N is, we can find n > N with .

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).
5. (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?
6. (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 such that however large N is, we can find n > N with .

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
7. (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!
8. (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
9. (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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