Première S2 Exercices sur le chapitre 16 : E2. 2007 2008
E2 Savoir calculer des termes d'une suite.
P 104 n ° 16 d.
un = ( - 1 )n u0 = ( - 1 )0 = 1 u1 = ( - 1 )1 = - 1 u2 = ( - 1 )2 = 1 u100 = ( - 1 )100 = 1.
P 104 n ° 17 a et d.
un = 3n² + n.
u0 = 3× 0² + 0 = 0.
u1 = 3× 1² + 1 = 3 + 1 = 4.
u2 = 3× 2² + 2 = 12 + 2 = 14.
u100 = 3 × 100² + 100 = 3 × 104 + 100 = 30100.
un = 1 − ( - 0,5 )n
u0 = 1 − ( - 0,5 )0 = 1 − 1 = 0 u1 = 1 − ( - 0,5 )1 = 1 + 0,5 = 1,5 u2 = 1 − ( - 0,5 )2 = 1 − 0,25 = 0,75 u100 = 1 − ( - 0,5 )100 = 1 − 100
21 . P 104 n ° 19 b . c.
u0 = 2
un+1 = ( un )² − 1
u0+1 = ( u0 )² − 1 = 4 − 1 = 3 u1+1 = ( u1 )² − 1 = 9 − 1 = 8 u2+1 = ( u2 )² − 1 = 64 − 1 = 63 u3+1 = ( u3 )² − 1 = 3969 − 1 = 3968 u0 = 2
un+1 = 1 u
u 2
n n
− +
u0+1 = ( 4 ) / ( 2 − 1 ) = 4
u1+1 = ( 2 + 4 ) / ( 4 − 1 ) = 6/3 = 2 u2+1 = ( 4 ) / ( 2 − 1 ) = 4
u3+1 = 2…
p 104 n ° 20.
22/7 ≈ 3,142857142857…
u1 = 1 u2 = 4 u3 = 2 u4 = 8 10 = 6 + 4 u10 = 8
100 = 6 × 16 + 4 u100 = 8
1001 = 6 × 166 + 5 u1001 = 5.
P 104 n ° 22.
vn = 2 n
n 3
² n−+ .
vn+1 =
2 1 n
) 1 n ( 3 )² 1 n (
+ +− +
+ =
3 n
3 n 3 1 n 2
²
n + ++− − vn+1 =
3 n
2 n
² n −+−
vn-1 =
2 1 n
) 1 n ( 3 )² 1 n (
+
−− −
− =
1 n
3 n 3 1 n 2
²
n − ++− + vn-1 =
1 n
4 n 5
² n−++
v0 = 0 v1 = - 2
3 v2 = - 2
4 = - 1 2 v3 = 0 v4 = 4
6 = 2 3
