| \[ k \ge 1 \quad a_0 \in \mathbb{R} \] | \[ S(n) = \] | |||
|---|---|---|---|---|
| formule récursive |
formule directe |
\[ \sum_{k=i}^{n} (a_k) \] | \[ \sum_{k=i}^{\infin} (a_k) \] | |
| arithmétique | \[ a_k = a_{k - 1} + r \] | \[ a_k = a_0 + r \cdot k \] | \[ \begin{aligned} nbt \cdot \frac{p + d}{2} \end{aligned} \] | |
| géométrique | \[ a_k = a_{k - 1} \cdot r \] | \[ a_k = a_0 \cdot r^k \\[1em] \] | \[ \frac{p - d \cdot r}{1 - r} \\[1em] \] | \[ \frac{a_0}{1 - r} \] |
| \[ \bigoplus \] | \[ \sum \] | \[ \prod \] |
|---|---|---|
| \[ \bigoplus_{k=1}^n (c) \] | \[ n c \] | \[ c^n \] |
| \[ \bigoplus_{k=1}^n (k) \] | \[ \frac{n (n + 1)}{2} \] | \[ n! \] |
| \[ \bigoplus_{k=1}^n (a_k \cdot c) \] | \[ c \cdot \sum_{k=1}^n (a_k) \] | \[ c^n \cdot \prod_{k=1}^n (a_k) \] |
| \[ \bigoplus_{k=i}^n \bigoplus_{l=j}^m (a_k \cdot b_l) = \bigoplus_{k=i}^n (a_k) \cdot \bigoplus_{l=j}^m (b_l) \\[1em] \] | ||
| \[ \begin{aligned} \bigoplus_{k=i}^n (a_k \oplus b_k) \quad = \quad \bigoplus_{k=i}^n (a_k) ~ \oplus ~ \bigoplus_{k=i}^n (b_k) \end{aligned} \] | ||
| \[ \begin{aligned} \orange{\bigoplus_{k=i}^n} \blue{\bigotimes_{l=j}^m} (a_{\orange{i} \blue{j}}) \quad = \quad \blue{\bigotimes_{l=j}^m} \orange{\bigoplus_{k=i}^n} (a_{\orange{i} \blue{j}}) \end{aligned} \] | ||
| \[ \begin{aligned} & \bigoplus_{i = 1}^n \bigoplus_{\orange{j = i}}^n (a_{ij}) \quad = \quad \bigoplus_{j = 1}^n \bigoplus_{i = 1}^\orange{j} (a_{ij}) \end{aligned} \] | ||