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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 $\{a_{n}\}$.

Can anyone please help me?

I'm completely lost...

Thanks in advance

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@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
up vote 0 down vote accepted

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?).

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