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Vojtěch Jarník IMC
2004 VJIMC
Problem 2
infinite arctan sum
infinite arctan sum
Source: VJIMC 2004 1.2
July 2, 2021
Summation
Sum
real analysis
Problem Statement
Evaluate the sum
∑
n
=
0
∞
arctan
(
1
1
+
n
+
n
2
)
.
\sum_{n=0}^\infty\operatorname{arctan}\left(\frac1{1+n+n^2}\right).
n
=
0
∑
∞
arctan
(
1
+
n
+
n
2
1
)
.
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