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
?