Update cheatsheet.fr.md

12.temporary_ins/04-math-tools/70.systems-of-differential-equations/40.parallel-1/cheatsheet.fr.md

@@ -68,14 +68,17 @@ $`M^0 = I_m`$ matrice identité de dimension $`m\times m`$.
 
 $`M`$ est diagonale :
 
-$`\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}`$
+$`M = \begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}`$
 
-$`\begin{align} M = &  e^{\,M} = 
+$`\begin{align} e^{\,M} = & \sum_{n=0}^{+\infty}\dfrac{M^n}{n!} \\
+\\
 \begin{pmatrix} 1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & 1 \\ \end{pmatrix} + 
 \begin{pmatrix}  \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix} + \cdots \\
 & \\
-& +\dfrac{1}{2!}\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}^2
-+\cdots + \dfrac{1}{k!}\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}^k + \cdots
+& \cdot +\dfrac{1}{2!}\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}^2
++\cdots \\
+\\
+& \cdot + \dfrac{1}{k!}\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}^k + \cdots
 \end{align}`$