A series is an infinite sum of sequence \((a_n)_{n\in \mathbb{N}}\) with suitable values. We write \(\sum_{n=0}^{\infty} a_n\) (even if this notion only makes sense if the series is convergent ).
A series can be considered as the sequence of its partial sums \((\sum_{n=0}^{N} a_n)_{N\in \mathbb{N}}\).