MathDB
Problems
Contests
National and Regional Contests
China Contests
ASDAN Math Tournament
2015 ASDAN Math Tournament
14
2015 Team #14
2015 Team #14
Source:
August 3, 2022
2015
team test
Problem Statement
For a given positive integer
m
m
m
, the series
∑
k
=
1
,
k
≠
m
∞
1
(
k
+
m
)
(
k
−
m
)
\sum_{k=1,k\neq m}^{\infty}\frac{1}{(k+m)(k-m)}
k
=
1
,
k
=
m
∑
∞
(
k
+
m
)
(
k
−
m
)
1
evaluates to
a
b
m
2
\frac{a}{bm^2}
b
m
2
a
, where
a
a
a
and
b
b
b
are positive integers. Compute
a
+
b
a+b
a
+
b
.
Back to Problems
View on AoPS