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Tuymaada Olympiad
1997 Tuymaada Olympiad
5
(1+1/q)(1+1/q^2)...(1+1/q^n)< (q-1)/(q-2)
(1+1/q)(1+1/q^2)...(1+1/q^n)< (q-1)/(q-2)
Source: Tuymaada 1997 p5
April 28, 2019
algebra
inequalities
Problem Statement
Prove the inequality
(
1
+
1
q
)
(
1
+
1
q
2
)
.
.
.
(
1
+
1
q
n
)
<
q
−
1
q
−
2
\left(1+\frac{1}{q}\right)\left(1+\frac{1}{q^2}\right)...\left(1+\frac{1}{q^n}\right)<\frac{q-1}{q-2}
(
1
+
q
1
)
(
1
+
q
2
1
)
...
(
1
+
q
n
1
)
<
q
−
2
q
−
1
for
n
∈
N
,
q
>
2
n\in N, q>2
n
∈
N
,
q
>
2
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