énoncé

u∈ L(E, F ){0E}
u∈ L(E, F )u E
F
x−2y= 3
ax −by =c
a b c [[1,6]]
a b c
(x, y) = (3,0)
π
π
π
x∈Rn∈N
Arctanx=
n
X
k=0
(−1)kx2k+1
2k+ 1 + (−1)n+1 Zx
0
t2n+2
1 + t2dt.
t∈R
n
P
k=0
(−1)kt2k
x∈[0,1] Zx
0
t2n+2
1 + t2dt −→
n→+∞0
+∞
X
k=0
(−1)k
2k+ 1 =π 4·

N1
π−4
N1
X
k=0
(−1)k
2k+ 1
61
107·
Pαn
π
6·
αn=4
6
(−1)n
2n+ 1 αn=(π
6si n= 0
0 sinon
N2
π−6
N2
X
k=0
αk 61
107·
N2N1
π10−7
0
1
0 1 1
0 1
0 1
1
1 0
1 1
1
Ek
2k+ 1 1
pk=P(Ek)
p0
k∈N2k+ 2 P(Ek+1|Ek)
k∈Npkpk+1 pk
\
k∈N
Ek
Ek∩Ek+1
Fk
2k+ 1 (1,1,1)
P(2k+ 1)P(Fk)
M Fk

x∈]−1,1[ n∈N
n
X
k=0
xk
n
X
k=0
kxk−1
∞
X
k=0
kxk−1.
M
qk
2k+ 1 1
k∈Nqk+1 =1
9qk+2 9·qkk
+∞
k∈Nrk2k0
n∈Nαnβnγnδnn
1 0 1 2 3
δ2k+1 =qkα2k=rk
n∈Nβn+1 αnγn
A∈ M4(R)
Xn=
αn
βn
γn
δn
Xn+1 =AXn
λ∈RA−λI4
uR4A
λ u −λR
?
?
?
1
R4u
P∈4(R)P−1AP P −1
An(A2n)n∈N(A2n+1)n∈N
(X2n)n∈N(X2n+1)n∈N
P−1
1
0