MathDB
Problems
Contests
Undergraduate contests
Putnam
1966 Putnam
B3
Putnam 1966 B3
Putnam 1966 B3
Source:
April 6, 2022
college contests
Problem Statement
Show that if the series
∑
n
=
1
∞
1
p
n
\sum_{n=1}^{\infty} \frac{1}{p_n}
n
=
1
∑
∞
p
n
1
is convergent, where
p
1
,
p
2
,
p
3
,
…
,
p
n
,
…
p_1,p_2,p_3,\dots, p_n, \dots
p
1
,
p
2
,
p
3
,
…
,
p
n
,
…
are positive real numbers, then the series
∑
n
=
1
∞
n
2
(
p
1
+
p
2
+
⋯
+
p
n
)
2
p
n
\sum_{n=1}^{\infty} \frac{n^2}{(p_1+p_2+\dots +p_n)^2}p_n
n
=
1
∑
∞
(
p
1
+
p
2
+
⋯
+
p
n
)
2
n
2
p
n
is also convergent.
Back to Problems
View on AoPS