Enoncé 2

x7→ 3x+ 1
8 arctan(1
2)−4 arctan(1 7)
fn(x) = exp( x
n)n1 10
n≥1un=
n
X
k=1
1
k2
limn→∞ un
π2
6n
unn≥1n≤0
r r ≤0n
|un−π2
6|< r
P=a0+a1X+· · · +anXn
[a0, a1, . . . , an]X+ 2X2−3X4
x P (x) = a0+a1x+· · · +anxn
P x
∀x∈R, P (x) = a0+x(a1+x(a2+x(. . . (an−1+xan). . . ))) .

x P P (x)
P(x) = a0+x×Q(x)Q
P= 1 + 1
2X+1 4X2+
· · · +1
210 X10 x= 3 P