Travaux dirigés MT11

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1
1
PQ
P⇒Q
4
(a)∃x∈R∀y∈Rx+y>0;(b)∀x∈R∃y∈Rx+y>0;
(c)∀x∈R∀y∈Rx+y>0;(d)∃x∈R∀y∈Ry2>x.
abcd
f,gR R
f
f
f
f
f
f
fN
fg
fg
32n+2 −2n+1
7n∈N
p1,p2, . . . , pr,r
N=1+p1p2. . . prpi
ABE
A∪B=A∩BA∩B=A∪B

1
n
n
X
k=1
k=n(n+1)
2∀n∈N∗.
n
X
k=1
k2=n(n+1)(2n+1)
6∀n∈N∗.
100
1+2+. . . +99 +100
100 +99 +. . . +2+1
101 +101 +. . . +101 +101
⇒1+2+··· +100 =1
2(101 ×100) =5050
n
Pn+1
k=1 k3−Pn k=0(k+1)3
n
Pn
k=0 k3
EnCk
nn
k
Ekn
k
A={x1,x2,...,xk}E
x1,...,xk(x1,x2,...,xk)x1,x2,...,xk
(x2,x1,...,xk)
(x1,x2,...,xk)
n
kkE
A={x1,x2,...,xk}Ek
A
n
k=n!
k!(n−k)!