Serie (mathematica)

In mathematica, plus precisemente in analyse mathematic, un serie es un sequentia consistente de summas ininterrupte, per exemplo ${\displaystyle 1+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{4}}+{\frac {1}{5}}+{\frac {1}{6}}+\dots }$ da como resultato le serie ${\displaystyle (1;\;1,5;\;1,8{\overline {3}};\;2,08{\overline {3}};\;2,28{\overline {3}};\;2,45;\;\dots )}$.

Le serie ${\displaystyle {\tfrac {1}{2}}+{\tfrac {1}{4}}+{\tfrac {1}{8}}+{\tfrac {1}{16}}+\ldots }$ converge a 1.

Serie
instantia de: concepto mathematic[*]
subclasse de: Summa, infinite expression[*]
Commons: Series (mathematics)

Definition

Sia ${\displaystyle \left(a_{i}\right)_{i\in \mathbb {N} }}$ un sequentia. Tunc le serie es le sequentia ${\displaystyle \left(s_{n}\right)_{i\in \mathbb {N} }}$ del summas partial:

le ${\displaystyle n}$-me summa partial es le summa del prime elementos ${\displaystyle n+1}$ del sequentia date ${\displaystyle \left(a_{i}\right)_{i\in \mathbb {N} }}$: ${\displaystyle s_{0}=a_{0}}$, ${\displaystyle s_{1}=a_{0}+a_{1}}$, ${\displaystyle s_{2}=a_{0}+a_{1}+a_{2}}$, ..., ${\displaystyle s_{n}=a_{0}+a_{1}+a_{2}+\dots +a_{n}}$, alora ${\displaystyle s_{n}=\sum _{i=0}^{n}a_{i}}$.