# Prove,( Sequence )

1. Apr 3, 2009

### remaan

1. The problem statement, all variables and given/known data

I have no idea
I wish If someone can help me with proving that the limit of nth term of a seq. an = to the limit of an+1

2. Relevant equations

we might use that an is greater of smaller than the other term wich is an+1

3. The attempt at a solution
we might suppose any sequn. ??

2. Apr 3, 2009

### CompuChip

You could use the definition of limit.

$$\lim_{n \to \infty} a_n = L$$
iff for any $\epsilon > 0$ there exists an $N = N_\epsilon$ such that $|a_n - L| < \epsilon$ whenever n > N.

Now suppose that
$$\lim_{n \to \infty} a_n = L$$
and let $\epsilon > 0$.
Can you now prove that
$$\lim_{n \to \infty} a_{n + 1} = L$$
?

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