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National and Regional Contests
Bosnia Herzegovina Contests
Bosnia Herzegovina Team Selection Test
2017 Bosnia Herzegovina Team Selection Test
3
3
Part of
2017 Bosnia Herzegovina Team Selection Test
Problems
(1)
Problem with sequences
Source: Bosnia Herzegovina TST 2017, problem 3
7/22/2017
Find all real constants c for which there exist strictly increasing sequence
a
a
a
of positive integers such that
(
a
2
n
−
1
+
a
2
n
)
/
a
n
=
c
(a_{2n-1}+a_{2n})/{a_n}=c
(
a
2
n
−
1
+
a
2
n
)
/
a
n
=
c
for all positive intеgers n.
algebra