TD 7 : Suites

(un)`
∀ > 0,∃N∈N,∀n∈N, n ≥N⇒ |un−`| ≤ 
1
n
1
2n
(un) (u2n) (u2n+1)
`(un)`
(un) (vn)
•(un)
•(vn)
•lim
n→+∞
un−vn= 0
(un) (vn)
n∈Nun≤vn
(un)`
(vn)`0
`=`0
un=
n
X
k=1
1
n+kvn=
2n
X
k=n
1
k
n∈N∗1
n+ 1 ≤ln n+ 1 n≤1 n
n∈N∗un≤ln(2) ≤vn