Ivan Shishkin, Rye (1878)

Problems/Set theoryExercise

Une somme avec des symboles de Kronecker

by Ancient Tree·
28
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  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
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Calculer la somme suivante de symboles de Kronecker :
∑i=15δi,3.\sum_{i=1}^{5} \delta_{i,3}.

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Solution by darktoaster

Discussions1 useful vote

∑i=15δi,3=δ1,3+δ2,3+δ3,3+δ4,3+δ5,3=0+0+1+0+0=1\sum\limits_{i=1}^5 \delta_{i,3} = \delta_{1,3} + \delta_{2,3}+\delta_{3,3}+\delta_{4,3}+\delta_{5,3} = 0 + 0 + 1 + 0 + 0 = 1
\newline
En effet par définition du symbole de Kronecker : δi,j={1, si i=j0, si i≠j\delta_{i,j} = \begin{cases} 1 \text{, si } i = j \\ 0 \text{, si } i \ne j \end{cases}
En particulier ∀i∈[ ⁣[1,5] ⁣],δi,3={1, si i=30, si i≠3\forall i \in [\![1,5]\!], \delta_{i,3} = \begin{cases} 1 \text{, si } i = 3 \\ 0 \text{, si } i \ne 3 \end{cases}

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