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Miklós Schweitzer
1960 Miklós Schweitzer
5
Miklós Schweitzer 1960- Problem 5
Miklós Schweitzer 1960- Problem 5
Source:
November 18, 2015
college contests
Problem Statement
5. Define the sequence
{
c
n
}
n
=
1
∞
\{c_n\}_{n=1}^{\infty}
{
c
n
}
n
=
1
∞
as follows:
c
1
=
1
2
c_1= \frac {1}{2}
c
1
=
2
1
,
c
n
+
1
=
c
n
−
c
n
2
c_{n+1}= c_{n}-c_{n}^2
c
n
+
1
=
c
n
−
c
n
2
(
n
≥
1
n\geq 1
n
≥
1
). Prove that
lim
n
→
∞
n
c
n
=
1
\lim_{n \to \infty} nc_n= 1
lim
n
→
∞
n
c
n
=
1
(S.12)
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