Tail of Convergent Sequence

Theorem
Let $\langle{a_n}\rangle$ be a real sequence.

Let $N \in \N$ be a natural number.

Let $a \in R$ be a real number.

Then:
 * $a_n \to a$


 * $a_{n + N} \to a$
 * $a_{n + N} \to a$