QCM corrigé suites et série de fonctions numériques
QCM
Suites
et
s
é
r
i
e
s
de
fonctions
numeriques
...
Question
s
(
1
,
2
,
3
)
l
i
é
es
Question
s
(
4
,
5
,
6
)
l
i
é
es
Question
1
Soit
f
une
fonction
continue
sur
0
,
1
à
valeurs
dans
ℝ
.
On
d
é
finit
∀
n
∈
ℕ
la
suite
de
fonction
f
n
x
=
e
−
nx
1
+
x
pour
x
∊
0
,
+
∞
la
suite
de
fonction
f
n
converge
□
uniform
é
ment
sur
0
,
+
∞
.
□
uniform
é
ment
sur
0
,
1
et
la
fonction
lim
ite
est
continue
.
□
uniform
é
ment
sur
0
,
+
∞
et
la
fonction
lim
ite
est
continue
.
□
uniform
é
ment
sur
tout
compact
de
0
,
+
∞
.
Question
2
Soit
v
n
=
∫
0
1
f
n
x
dx
□
la
suite
v
n
converge
car
0
≤
v
n
≤
1
1
+
x
.
□
la
suite
v
n
converge
car
0
≤
v
n
≤
1
−
e
−
n
n
.
□
la
suite
v
n
converge
vers
1
.
□
la
suite
v
n
converge
car
il
est
croissante
est
major
é
e
Question
3
Soit
ω
n
=
∫
0
1
nx
n
f
x
dx
□
la
suite
ω
n
converge
vers
1
.
□
la
suite
ω
n
converge
si
f
est
un
polynome
.
□
la
suite
ω
n
converge
vers
+
∞
si
f
est
positive
□
lim
ω
n
n
→
+
∞
=
f
1
Question
4
Le
rayon
de
convergence
de
la
serie
enti
é
re
∑
n
=
1
∞
n
n
−
1
!
x
n
vaut
:
□
ρ
=
1
□
ρ
=
∞
□
ρ
=
0
□
ρ
=
exp
2
Question
5
Pour
x
<
ρ
la
somme
∑
n
=
1
∞
n
n
−
1
!
x
n
vaut
:
□
x
2
e
x
□
x
2
−
x
e
x
□
x
2
+
x
e
x
□
x
2
−
x
e
2
x
Question
6
La
serie
∑
n
=
1
∞
n
−
2
n
n
−
1
!
:
□
est
convergente
mais
pas
absolument
convergente
□
est
convergente
donc
absolument
convergente
□
est
absolument
convergente
donc
convergente
□
n
'
est
ni
convergente
ni
absolument
convergente
Question
7
∑
n
=
1
∞
n
π
n
+
1
vaut
:
□
π
π
−
1
□
1
π
−
1
2
□
π
π
−
1
2
□
1
π
2
−
1
Question
8
lim
n
→
+
∞
∫
0
n
1
−
x
n
n
dx
=
□
0
□
e
□
1
/
e
□
1
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Bonjour !!!!!!
RépondreEffacerLes QCM sont super interressants mais malheueusement sans correction.
Ou puis je avoir les CORRECTIONS svp
Cordialement Dobi55555
La correction s'il vous plait
RépondreEffacer