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International Contests
Tournament Of Towns
1997 Tournament Of Towns
(551) 1
(551) 1
Part of
1997 Tournament Of Towns
Problems
(1)
TOT 551 1997 Autumn J A1 x_{n+2} =x_n - 1/x_{n+1}
Source:
9/11/2024
The sequence
x
1
,
x
2
,
.
.
.
x_1,x_2, ...
x
1
,
x
2
,
...
is defined by the following equations:
x
1
=
19
,
x
2
=
97
,
x
n
+
2
=
x
n
−
1
x
n
+
1
x_1=19, \ \ x_2=97, \ \ x_{n+2} =x_n - \frac{1}{x_{n+1}}
x
1
=
19
,
x
2
=
97
,
x
n
+
2
=
x
n
−
x
n
+
1
1
for
n
≥
1
n \ge 1
n
≥
1
. Prove that there exists a positive integer
k
k
k
such that
x
k
=
0
x_k=0
x
k
=
0
and find
k
k
k
. (A Berzinsh)
algebra
Sequence
recurrence relation