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IMC
2011 IMC
1
IMC 2011 Day 2, Problem 1
IMC 2011 Day 2, Problem 1
Source:
August 1, 2011
induction
IMC
college contests
Problem Statement
Let
(
a
n
)
⊂
(
1
2
,
1
)
(a_n)\subset (\frac{1}{2},1)
(
a
n
)
⊂
(
2
1
,
1
)
. Define the sequence
x
0
=
0
,
x
n
+
1
=
a
n
+
1
+
x
n
1
+
a
n
+
1
x
n
x_0=0,\displaystyle x_{n+1}=\frac{a_{n+1}+x_n}{1+a_{n+1}x_n}
x
0
=
0
,
x
n
+
1
=
1
+
a
n
+
1
x
n
a
n
+
1
+
x
n
. Is this sequence convergent? If yes find the limit.
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