Series (elementary mathematics)

The Séries are a category of Suite. A series of general term $u\_n$ is, basiquement, the sum of N first terms of the continuation $(u\_n)\; \_\; \{N\; \backslash \; in\; \backslash \; mathbb\; \{NR\}\}$. For this reason one calls the continuation $(S\_n)\; \_\; \{N\; \backslash \; in\; \backslash \; mathbb\; \{NR\}\}$, the continuation of the partial sums.

$S\_n=u\_0\; +\; u\_1\; +\dots \; +\; u\_n\; =\; \backslash \; sum\_\; \{k=0\}\; ^n\; u\_k$, where $u\_k$ is the term of index K of the continuation $(u\_n)\; \_\; \{N\; \backslash \; in\; \backslash \; mathbb\; \{NR\}\}$.

One notes this series $\backslash \; sum\; u\_n$.

The most traditional example with the college is the series defined by:

$S\_n=\backslash sum\_\{k=0\}^n\; U\_0.q^k=U\_0.\backslash frac\{1-q^\{n+1\}\}\{1-q\}$

I.e. the sum of the terms of a geometrical Continuation of reason $q$ and first $U\_0$ term.

Another example, the continuation defined for entire naturalness $n:\; U\_n=n$ has as an associated series:

$S\text{'}\_n=\; \backslash \; sum\_\; \{k=0\}\; ^n\; U\_k=0+1+2+\dots \; +n=\; \backslash \; frac\; \{N\; (n+1)\}\{2\}$

See also the article " geometrical Series "

Random links:

Canton of Deprived | Jamy Gourmaud | Theorem of Wick | Jone Qovu | Amateurs of Mickey | Théâtre_de_groupe_(New_York)

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