MathDB
Problems
Contests
National and Regional Contests
India Contests
Postal Coaching
2015 Postal Coaching
2
2
Part of
2015 Postal Coaching
Problems
(1)
Natural numbers in Harmonic Progression
Source: CIIM 2015, India Postal Coaching 2015
12/2/2015
Prove that there exists a real number
C
>
1
C > 1
C
>
1
with the following property. Whenever
n
>
1
n > 1
n
>
1
and
a
0
<
a
1
<
a
2
<
⋯
<
a
n
a_0 < a_1 < a_2 <\cdots < a_n
a
0
<
a
1
<
a
2
<
⋯
<
a
n
are positive integers such that
1
a
0
,
1
a
1
⋯
1
a
n
\frac{1}{a_0},\frac{1}{a_1} \cdots \frac{1}{a_n}
a
0
1
,
a
1
1
⋯
a
n
1
form an arithmetic progression, then
a
0
>
C
n
a_0 > C^n
a
0
>
C
n
.
number theory
bounded