PREPAsup

In=Zπ
2
0cosnxdx
I0, I1
InIn−2
I2p+1 I2p
Jn=
n
X
k=1
1
k(k+ 1)(k+ 2)
a, b, c 1
k(k+1)(k+2) =a k+b k+1 +c k+2
Jn
ωn=
n
Y
k=0
(ekx)
ω0, ω1, ω2ω3
ωn
Sn=
n
X
i=0
(
n
X
k=i
i
k+ 1)
Sn
fn(x) = Z1
0
1
(1 + x2)ndx
f0, f1f2
Pn(x) = (1 + x)n=
n
X
k=0
Ck
nxk

Pn(x)Pn
k=1 kCk n=n2n−1
Pn
k=2 k(k−1)Ck n=n(n−1)2n−2
P′(x)
φn=
n
X
k=0 Z1
0(−x)kdx
limn→+∞φn=ln2
f(x) = ex
1 + E(x)
f(x)
f(x) = 1 + x2
x+E(x)
f(x)
Pn(x) = 1
2nn!D(n)(x2−1)n
Pn(x)D(n)
P0(x), P1(x), P2(x)P3(x)
Un+1 =qUn−1
U0= 26 (Un)
(Un)
Un=
n
X
k=0
1
p!
∀p≥11
p!≤1 2p−1
(Un)
l
n
X
k=1
ap
k= (
n
X
k=1
ak)p
Sn=
2n
X
k=0
2kcos(kπ
2)

Sn
limn−→+∞Sn
Sn=
n
X
k=1
(−1)kk, Tn=
n
X
k=1
ln(1 + 1
k)
SnTn
zn+2 =zn+1 +n
zn
∀nϵIN ∗z1= 1 z2= 2
(zn)
(zn)
(zn)
vn=
n
X
p=0
(−1)p
p+ 1
vn+2 −vn
(v2n)nϵIN (v2n+1)nϵIN
(vn)
P(t) = (f(x)t+g(x))2
h(t) = ZP(t)
h(t) = Z(f(x))2t2+ 2 Z(f(x)g(x))t+Zg(x)2
Z(f(x)g(x))2≤Zf(x)2Zg(x)2

In=Z1
0
xnln(1 + x2)dx
I0, I1I2
lim
n−→+∞In= 0.
ϵ
An=Zc
0
xnln(1 + x2)dx, Bn=Z1
c
xnln(1 + x2)dx
lim
n−→+∞
An
Bn
= 0
g(x) = (1 + x)n
n
X
k=0
Ck
n
k+ 1 =2n+1 −1 n+ 1