Theorem states:

Note that a (sub n) is a constant sequence.

Suppose a (sub n) = a for all n greater than or equal to 1.

Then lim a (sub n) as n approaches infinity = a.

I need to prove this.

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- Mar 4th 2008, 06:23 PMCarolproof of a theorem
Theorem states:

Note that a (sub n) is a constant sequence.

Suppose a (sub n) = a for all n greater than or equal to 1.

Then lim a (sub n) as n approaches infinity = a.

I need to prove this. - Mar 4th 2008, 06:27 PMThePerfectHacker
- Mar 4th 2008, 06:36 PMJhevon
you need to use the definition of the limit for a sequence to show that $\displaystyle \lim_{n \to \infty}a_n = a$

that is, you must show that: for every $\displaystyle \epsilon > 0$, there exists an $\displaystyle N \in \mathbb{N}$ such that $\displaystyle n > N$ implies $\displaystyle |a_n - a|< \epsilon$