Relation between a sum of a series and the limit of a sequence

I'm stuck on this question

Let $\{a_{n}\}$ a sequence of real numbers

I need to show the series $\sum_{n=1}^{\infty}(a_{n} - a_{n-1})$ and the sequence $\{a_{n}\}$ are the same nature (convergent or divergent). Additional, I need to give a relation between the sum of the series and the limit of the sequence $\{a_{n}\}$.

I'm completely lost...

@labbhattacharjee: The question is about the sequence with entries $a_n$, not about the series with terms $a_n$. –  Marc van Leeuwen May 21 '13 at 9:49
Hint: What is the $k$-th partial sum of the series? (remember that a series converges to $L$ iff the sequence of its partial sums converges to $L$, so what will happen if you found out that the partial sums of the series give back the sequence of $a_n$'s?).