Nombres. • Trigonométrie. • Notations ∑ et ∏ , et formule du binôme

BCP ST 1B
•
R
•
−θ π −θπ
2−θ
cos(a+b) sin(a+b) cos(a−b) sin(a−b) cos(2θ) sin(2θ)
arccos arcsin arctan
cos(x) = tsin(x) = ttan(x) = t
acos(θ) + bsin(θ)rcos(θ+ϕ)acos(θ) + bsin(θ) = t
•P Q
(n∈Net q∈C\ {1})
n
X
k=0
qk=1−qn+1
1−q
n
X
k=0
k=n(n+ 1)
2
n
X
k=0
k2=n(n+ 1)(2n+ 1)
6
n
X
k=0
k3=n2(n+ 1)2
4
•n!n
p
(0 6p6n)n
p=n!
k!(n−k)! =n(n−1) · · · (n−p+ 1) p!=
p−1
Y
k=0
n−k
k+ 1 n p= 0
∀(n, p)∈N2,n+ 1
p+ 1=n p+n p+ 1∀(n, p)∈Z2, pn p=nn−1 p−1  n n−p=n p
n
kn!
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
n!n
k 17 15(n+ 1)!
(n−1)!
arccos arcsin arctan
cos(x) = asin(x) = atan(x) = a
n
k
n
X
k=0 n
kn
X
k=0 n
k(−1)k
n
X
k=0
kn
kn
X
k=0 k
p