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Vojtěch Jarník IMC
1995 VJIMC
Problem 4
limit of arctan^n(x)
limit of arctan^n(x)
Source: VJIMC 1995 2.4
November 25, 2021
limits
real analysis
trigonometry
Problem Statement
Let
{
x
n
}
n
=
1
∞
\{x_n\}_{n=1}^\infty
{
x
n
}
n
=
1
∞
be a sequence such that
x
1
=
25
x_1=25
x
1
=
25
,
x
n
=
arctan
(
x
n
−
1
)
x_n=\operatorname{arctan}(x_{n-1})
x
n
=
arctan
(
x
n
−
1
)
. Prove that this sequence has a limit and find it.
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