Exercices

P(N,P(N))
P({n})−→
n→+∞0
A B C
A
A B C
A1, A2An
AiN0
Ai
Aii>N0
Ai
E
A B C E
|A∪B∪C|=|A|+|B|+|C| − (|A∩B|+|A∩C|+|B∩C|) + |A∩B∩C|
[[1,4]] [[1,3]]
52

1,2, ..., n n
1 2
1,2 3
1 2
2
Cn,p SCn,p
p[[1, n]]
SCn,p
Φ:(u1, ..., up)∈Cn,p 7−→ (u1, u2+ 1, u3+ 2, ..., up+ (p−1))
Cn,p SCn+p−1,p
p n 1n
12 6
5pn
n
p1p2
(pn)n∈Npnn>1

n
n
k k + 2
5
U1U2
U1U2
n∈N∗Bnn pn=P(Bn)
p1
∀n∈N∗, pn+1 =−6
35pn+4 7·
pnn∈N∗
1 9
i>1Aii
∞
\
i=1
Ai
∞
[
i=42
Ai
n∈NDn
n
∞
\
n=1
Dn
∞
\
n=945
Dn
p∈]0,1[
1R∈ {A, B}

>9
66
5/6 4/5
1 1 n>1n
n+ 1
p∈]0,1[
1−p
2 1 p
3
pnn
pnpn
(pn)n∈N∗n+∞
P Q R
1/2n∈NXn=
pn
qn
rn
pnqnrn
n P Q R
pn+1 (pn, qn, rn)
p1p2p3

Xn+1 =AXnA
A2=1
2A+1 2I3Xn
(X+ 1/2)(X−1) An
XnX0
1/2
c=3
4
1/4
1/2
20% 10% 3
50% 1% 3
10% 2% 3
3 5%