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International Contests
Tuymaada Olympiad
1995 Tuymaada Olympiad
2
2
Part of
1995 Tuymaada Olympiad
Problems
(1)
max a wanted so that \lim_{n\to \infty} x_n exists where x_n=a^{x_{n-1}} , a>1
Source: Tuymaada 1995 p2
4/27/2019
Let
x
1
=
a
,
x
2
=
a
x
1
,
.
.
.
,
x
n
=
a
x
n
−
1
x_1=a, x_2=a^{x_1}, ..., x_n=a^{x_{n-1}}
x
1
=
a
,
x
2
=
a
x
1
,
...
,
x
n
=
a
x
n
−
1
where
a
>
1
a>1
a
>
1
. What is the maximum value of
a
a
a
for which lim exists
lim
n
→
∞
x
n
\lim_{n\to \infty} x_n
lim
n
→
∞
x
n
and what is this limit?
limit
Limit of sequence
recurrence relation
maximum
algebra