MathDB
Problems
Contests
Undergraduate contests
VTRMC
2018 VTRMC
6
Extrema of Difference of Sequences
Extrema of Difference of Sequences
Source: 2018 VTRMC P6
January 8, 2023
VTRMC
college contests
Sequences
extrema
maximum
minimum value
Problem Statement
For
n
∈
N
n \in \mathbb{N}
n
∈
N
, define
a
n
=
1
+
1
/
3
+
1
/
5
+
⋯
+
1
/
(
2
n
−
1
)
n
+
1
a_n = \frac{1 + 1/3 + 1/5 + \dots + 1/(2n-1)}{n+1}
a
n
=
n
+
1
1
+
1/3
+
1/5
+
⋯
+
1/
(
2
n
−
1
)
and
b
n
=
1
/
2
+
1
/
4
+
1
/
6
+
⋯
+
1
/
(
2
n
)
n
b_n = \frac{1/2 + 1/4 + 1/6 + \dots + 1/(2n)}{n}
b
n
=
n
1/2
+
1/4
+
1/6
+
⋯
+
1/
(
2
n
)
. Find the maximum and minimum of
a
n
−
b
n
a_n - b_n
a
n
−
b
n
for
1
≤
n
≤
999
1 \leq n \leq 999
1
≤
n
≤
999
.
Back to Problems
View on AoPS