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National and Regional Contests
Iran Contests
Iran MO (2nd Round)
1983 Iran MO (2nd round)
5
Sum of arctangents - [Iran Second Round 1983]
Sum of arctangents - [Iran Second Round 1983]
Source:
December 30, 2010
limit
Problem Statement
Find the value of
S
n
=
arctan
1
2
+
arctan
1
8
+
arctan
1
18
+
⋯
+
arctan
1
2
n
2
.
S_n= \arctan \frac 12 + \arctan \frac 18+ \arctan \frac {1}{18} + \cdots + \arctan \frac {1}{2n^2}.
S
n
=
arctan
2
1
+
arctan
8
1
+
arctan
18
1
+
⋯
+
arctan
2
n
2
1
.
Also find
lim
n
→
∞
S
n
.
\lim_{n \to \infty} S_n.
lim
n
→
∞
S
n
.
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