# A convergent sequence problem

• Nov 20th 2006, 12:40 PM
A 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, 01:07 PM
TD!
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, 03:16 PM
Plato
Using what TD has shown you, I would suggest $e = \frac{a}{2}.$
• Nov 20th 2006, 11:51 PM
TD!
I was hoping tttcomrader would be figuring out that himself ;)