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France Contests
French Mathematical Olympiad
1995 French Mathematical Olympiad
Problem 2
Problem 2
Part of
1995 French Mathematical Olympiad
Problems
(1)
convergence of sequence
Source: French MO 1995 P2
4/22/2021
Study the convergence of a sequence defined by
u
0
≥
0
u_0\ge0
u
0
≥
0
and
u
n
+
1
=
u
n
+
1
n
+
1
u_{n+1}=\sqrt{u_n}+\frac1{n+1}
u
n
+
1
=
u
n
+
n
+
1
1
for all
n
∈
N
0
n\in\mathbb N_0
n
∈
N
0
.
algebra
Sequences