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#5 Sommes et produits - Coggle Diagram
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\( \textbf{Sommes d'Euler} \\ E_1(n) = 1 + 2 + \dots + n = \frac{n(n+1)}{2} \\ E_2 = 1^2 + 2^2 + \dots + n^2 = \frac{n(n+1)(2n+1)}{6} \\ E_3 = 1^3 + 2^3 + \dots + n^3 = (\frac{n(n+1)}{2})^2 \)
\( \textbf{Relation de Fubini} \\ \sum_{m \leqslant k \leqslant \ell \leqslant n} u_{k, \ell} = \sum_{k = m}^n \sum_{\ell = k}^n u_{k, \ell} = \sum_{\ell = m}^n \sum_{k = m}^\ell u_{k, \ell} \)