Q: Let the sequence {An} converge to a with a>0, prove there exist an N within the set of natural numbers such that n >= N implies {An} > 0

thank you!

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- Nov 20th 2006, 11:40 AMtttcomraderA convergent sequence problem
Q: Let the sequence {An} converge to a with a>0, prove there exist an N within the set of natural numbers such that n >= N implies {An} > 0

thank you! - Nov 20th 2006, 12:07 PMTD!
The convergence of the sequence (A(n)) to a tells you that for all e > 0, there exists an N such that for all n > N, |A(n)-a| < e.

This last statement is equivalent to saying that a-e < A(n) < a+e, but you know that a > 0.

Now just take the e > 0 small enough such that a > e which implies a-e > 0 and thus A(n) > 0. - Nov 20th 2006, 02:16 PMPlato
Using what TD has shown you, I would suggest $\displaystyle e = \frac{a}{2}.$

- Nov 20th 2006, 10:51 PMTD!
I was hoping tttcomrader would be figuring out that himself ;)