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MacBook-Pro-de-Oscar.local 2025-7-27:20:45:12

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2025-07-27 20:45:12 +02:00
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---
documentclass: beamer
header-includes:
\usepackage{amsmath, amssymb, amsfonts, mathrsfs}
\usepackage{svg}
tags: ["s/maths"]
---
--- ---
# 1 2 4 8 ... et après ? # 1 2 4 8 ... et après ?
--- ---
# Première réponse # Première réponse
1, 2, 3, 4, 8, 16, 32... 1, 2, 3, 4, 8, 16, 32...
--- ---
# Puissances de Deux # Puissances de Deux
1, 2, 4, 8, 16, 32... 1, 2, 4, 8, 16, 32...
@@ -18,6 +27,7 @@
- C'est la suite des puissances de $2$ - C'est la suite des puissances de $2$
--- ---
# Puissances de Deux # Puissances de Deux
1, 2, 4, 8, 16, 32... 1, 2, 4, 8, 16, 32...
@@ -28,11 +38,14 @@
- la partie remporte 1, puis 2, puis 4 etc... - la partie remporte 1, puis 2, puis 4 etc...
--- ---
![[de Videau.png]] \includegraphics{images/de Videau.png}
--- ---
# Autres réponses # Autres réponses
--- ---
# Somme des chiffres des puissances de 2 # Somme des chiffres des puissances de 2
**1, 2, 4, 8, 7, 5, 10, 11, 13**, 8, 7, 14, 19, 20, 22, 26, 25, 14, 19, 29, 31, 26, 25, 41 **1, 2, 4, 8, 7, 5, 10, 11, 13**, 8, 7, 14, 19, 20, 22, 26, 25, 14, 19, 29, 31, 26, 25, 41
@@ -49,6 +62,7 @@
| $\vdots$ | $\vdots$ | | $\vdots$ | $\vdots$ |
--- ---
# Somme de tous les chiffres précédents # Somme de tous les chiffres précédents
**1, 1, 2, 4, 8, 16, 23,** 28, 38, 49, 62, 70, 77, 91, 101, 103, 107, 115, 122, 127, 137 ... **1, 1, 2, 4, 8, 16, 23,** 28, 38, 49, 62, 70, 77, 91, 101, 103, 107, 115, 122, 127, 137 ...
@@ -67,6 +81,7 @@
| $\vdots$ | $\vdots$ | | $\vdots$ | $\vdots$ |
--- ---
# Partie entière de $\frac{n^{\;2}}{2}$ # Partie entière de $\frac{n^{\;2}}{2}$
0, 0, **2**, **4**, **8**, 12, 18, 24 ... 0, 0, **2**, **4**, **8**, 12, 18, 24 ...
@@ -82,6 +97,7 @@ $n \mapsto \left\lfloor \dfrac{n^{2}}{2} \right\rfloor$
| $\vdots$ | $\vdots$ | | $\vdots$ | $\vdots$ |
--- ---
# U # U
**1, 2, 4, 8, 9, 12, 14, 15 ...** **1, 2, 4, 8, 9, 12, 14, 15 ...**
@@ -89,16 +105,21 @@ les nombres qui s'écrivent avec "u"
--- ---
# Arbres ternaires à n points # Arbres ternaires à n points
![[arbres ternaires.excalidraw|700]]
\includesvg{Excalidraw/arbres ternaires.excalidraw.svg}
--- ---
# Cercles # Cercles
Nombre de régions avec $n$ cercles Nombre de régions avec $n$ cercles
**1, 2, 4, 8**, 14, 22, 32... **1, 2, 4, 8**, 14, 22, 32...
![[nombre de régions avec n+1 cercles.excalidraw|700]]
\includesvg{Excalidraw/nombre de régions avec n+1 cercles.excalidraw.svg}
--- ---
# Puissances d'une racine de 18 # Puissances d'une racine de 18
**1, 2, 4, 8**, 17, 37, 76, 157... **1, 2, 4, 8**, 17, 37, 76, 157...
$n \mapsto \left\lfloor \left(\sqrt{\sqrt{18}}\right)^{n} \right\rfloor$ $n \mapsto \left\lfloor \left(\sqrt{\sqrt{18}}\right)^{n} \right\rfloor$
@@ -107,6 +128,7 @@ $\sqrt{\sqrt{18}} \approx 2.059767144$
--- ---
# Diviseurs # Diviseurs
Diviseurs de 88 : **1, 2, 4, 8**, 11, 22, 44, 88 Diviseurs de 88 : **1, 2, 4, 8**, 11, 22, 44, 88
@@ -128,6 +150,7 @@ Diviseurs de 832 : **1, 2, 4, 8**, 13, 16, 26, 32, 52,  64, 104, 208, 416, 832
Diviseurs de 136 : **1, 2, 4, 8**, 17, 34, 68, 136. Diviseurs de 136 : **1, 2, 4, 8**, 17, 34, 68, 136.
--- ---
# Polynômes de Lagrange # Polynômes de Lagrange
1, 2, 4, 8, 11 --> $-\frac{1}{6}x^{4} + \frac{11}{6}x^{3} – \frac{19}{3} x^2 + \frac{29}{3} x -4$ 1, 2, 4, 8, 11 --> $-\frac{1}{6}x^{4} + \frac{11}{6}x^{3} – \frac{19}{3} x^2 + \frac{29}{3} x -4$
@@ -142,5 +165,6 @@ Diviseurs de 136 : **1, 2, 4, 8**, 17, 34, 68, 136.
1, 2, 4, 8, 20 --> $\frac{5}{24}x^{4} – \frac{23}{12}x^{3} + \frac{163}{24}x^{2} - \frac{109}{12}x+5$ 1, 2, 4, 8, 20 --> $\frac{5}{24}x^{4} – \frac{23}{12}x^{3} + \frac{163}{24}x^{2} - \frac{109}{12}x+5$
--- ---
# Il y en a plein ! # Il y en a plein !

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---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
## Drawing
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```
%%

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Excalidraw/nombre de régions avec n+1 cercles.excalidraw.md
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==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== ==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
# Text Elements # Excalidraw Data
## Text Elements
%% %%
# Drawing ## Drawing
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