proof 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.

Quote:

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Originally Posted by Carol

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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Is it true that ?

Quote:

---

Originally Posted by Carol

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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you need to use the definition of the limit for a sequence to show that

that is, you must show that: for every , there exists an such that implies