MathDB
Problems
Contests
Undergraduate contests
Putnam
1948 Putnam
A3
Putnam 1948 A3
Putnam 1948 A3
Source: Putnam 1948
March 15, 2022
Putnam
Sequences
series
Problem Statement
Let
(
a
n
)
(a_n)
(
a
n
)
be a decreasing sequence of positive numbers with limit
0
0
0
such that
b
n
=
a
n
−
2
a
n
+
1
+
a
n
+
2
≥
0
b_n = a_n -2 a_{n+1}+a_{n+2} \geq 0
b
n
=
a
n
−
2
a
n
+
1
+
a
n
+
2
≥
0
for all
n
.
n.
n
.
Prove that
∑
n
=
1
∞
n
b
n
=
a
1
.
\sum_{n=1}^{\infty} n b_n =a_1.
n
=
1
∑
∞
n
b
n
=
a
1
.
Back to Problems
View on AoPS