Prove Sequence: Limit an=Limit an+1

[remaan]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

we might suppose any sequn. ??

 

[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
$$\lim_{n \to \infty} a_{n + 1} = L$$
?