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Summa

De Wikipedia, le encyclopedia libere
Summa
instantia de:iterated binary operation[*],algebra,operation[*]
subclasse de:weighted sum[*],operation result[*]
parte de:mathematica,addition


Commons:Summation

Unsumma[1] es le resultato de unaddition. Anque le resultato de unserie es un summa. Pro additiones longe e regular, on usa le symboloΣ{\displaystyle \Sigma }, lege:sigma.

Per exemplo,∑i=16i=1+2+3+4+5+6=21{\displaystyle \sum _{i=1}^{6}i=1+2+3+4+5+6=21}.

In general, pro omnen∈N{\displaystyle n\in \mathbb {N} } es ver∑i=1ni=n(n+1)2{\displaystyle \sum _{i=1}^{n}i={\frac {n(n+1)}{2}}}.

In le exemplo:∑i=16i=6(6+1)2=6⋅72=422=21{\displaystyle \sum _{i=1}^{6}i={\frac {6(6+1)}{2}}={\frac {6\cdot 7}{2}}={\frac {42}{2}}=21}.

Un altere exemplo:∑i=1100i=100(100+1)2=5050{\displaystyle \sum _{i=1}^{100}i={\frac {100(100+1)}{2}}=5050}.

Referentias

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  1. ↑Derivation (in ordine alphabetic):(ca) Sumatori ||(de) Summe ||(en) Summation ||(es) Sumatorio ||(fr) Somme (arithmétique) ||(it) Sommatoria ||(pt) Somatório ||(ro) Sumă||(ru) Сумма (математика)
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