MathDB
Problems
Contests
International Contests
Kvant Problems
Kvant 2022
M2726
M2726
Part of
Kvant 2022
Problems
(1)
Iterated fractions
Source: Kvant Magazine No. 11-12 2022 M2726
3/7/2023
Let
a
1
=
1
a_1=1
a
1
=
1
and
a
n
+
1
=
2
/
(
2
+
a
n
)
a_{n+1}=2/(2+a_n)
a
n
+
1
=
2/
(
2
+
a
n
)
for all
n
⩾
1
n\geqslant 1
n
⩾
1
. Similarly,
b
1
=
1
b_1=1
b
1
=
1
and
b
n
+
1
=
3
/
(
3
+
b
n
)
b_{n+1}=3/(3+b_n)
b
n
+
1
=
3/
(
3
+
b
n
)
for all
n
⩾
1
n\geqslant 1
n
⩾
1
. Which is greater between
a
2022
a_{2022}
a
2022
and
b
2022
b_{2022}
b
2022
?Proposed by P. Kozhevnikov
Kvant
algebra