n

R_n

u_n

S_n

Activité\;1

\;\;\;\;\;\;Conjecture:\;\;\;S_n\;=\;R_{n}^{2}\
donc\;\;S_n\;=\;\left(1+2+3+...+n   \right) ^2

A2:0
A3: A2 + 1
A4: A3 + 1
A5: A4 + 1
A6: A5 + 1
A7: A6 + 1
A8: A7 + 1
A9: A8 + 1
A10: A9 + 1
A11: A10 + 1
A12: A11 + 1
A13: A12 + 1
A14: A13 + 1
A15: A14 + 1
A16: A15 + 1
A17: A16 + 1
A18: A17 + 1
A19: A18 + 1
A20: A19 + 1
A21: A20 + 1
A22: A21 + 1
A23: A22 + 1
A24: A23 + 1
A25: A24 + 1
A26: A25 + 1
A27: A26 + 1
A28: A27 + 1
A29: A28 + 1
A30: A29 + 1
A31: A30 + 1
A32: A31 + 1
B2:0
B3: B2 + A3
B4: B3 + A4
B5: B4 + A5
B6: B5 + A6
B7: B6 + A7
B8: B7 + A8
B9: B8 + A9
B10: B9 + A10
B11: B10 + A11
B12: B11 + A12
B13: B12 + A13
B14: B13 + A14
B15: B14 + A15
B16: B15 + A16
B17: B16 + A17
B18: B17 + A18
B19: B18 + A19
B20: B19 + A20
B21: B20 + A21
B22: B21 + A22
B23: B22 + A23
B24: B23 + A24
B25: B24 + A25
B26: B25 + A26
B27: B26 + A27
B28: B27 + A28
B29: B28 + A29
B30: B29 + A30
B31: B30 + A31
B32: B31 + A32
C2: A2^(3)
C3: A3^(3)
C4: A4^(3)
C5: A5^(3)
C6: A6^(3)
C7: A7^(3)
C8: A8^(3)
C9: A9^(3)
C10: A10^(3)
C11: A11^(3)
C12: A12^(3)
C13: A13^(3)
C14: A14^(3)
C15: A15^(3)
C16: A16^(3)
C17: A17^(3)
C18: A18^(3)
C19: A19^(3)
C20: A20^(3)
C21: A21^(3)
C22: A22^(3)
C23: A23^(3)
C24: A24^(3)
C25: A25^(3)
C26: A26^(3)
C27: A27^(3)
C28: A28^(3)
C29: A29^(3)
C30: A30^(3)
C31: A31^(3)
C32: A32^(3)
D2:0
D3: D2 + C3
D4: D3 + C4
D5: D4 + C5
D6: D5 + C6
D7: D6 + C7
D8: D7 + C8
D9: D8 + C9
D10: D9 + C10
D11: D10 + C11
D12: D11 + C12
D13: D12 + C13
D14: D13 + C14
D15: D14 + C15
D16: D15 + C16
D17: D16 + C17
D18: D17 + C18
D19: D18 + C19
D20: D19 + C20
D21: D20 + C21
D22: D21 + C22
D23: D22 + C23
D24: D23 + C24
D25: D24 + C25
D26: D25 + C26
D27: D26 + C27
D28: D27 + C28
D29: D28 + C29
D30: D29 + C30
D31: D30 + C31
D32: D31 + C32
liste1: {A1, A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18, A19, A20, A21, A22, A23, A24, A25, A26, A27, A28, A29, A30, A31, A32, C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, C12, C13, C14, C15, C16, C17, C18, C19, C20, C21, C22, C23, C24, C25, C26, C27, C28, C29, C30, C31, C32}
A: (A2, C2)
B: (A3, C3)
C: (A4, C4)
D: (A5, C5)
E: (A6, C6)
F: (A7, C7)
G: (A8, C8)
H: (A9, C9)
I: (A10, C10)
J: (A11, C11)
K: (A12, C12)
L: (A13, C13)
M: (A14, C14)
N: (A15, C15)
O: (A16, C16)
P: (A17, C17)
Q: (A18, C18)
R: (A19, C19)
S: (A20, C20)
T: (A21, C21)
U: (A22, C22)
V: (A23, C23)
W: (A24, C24)
Z: (A25, C25)
A_1: (A26, C26)
B_1: (A27, C27)
C_1: (A28, C28)
D_1: (A29, C29)
E_1: (A30, C30)
F_1: (A31, C31)
G_1: (A32, C32)
a = PolyLine({A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1})