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Mathematics
Mathematics
Problem
The value of
∑
r
=
1
∞
tan
−
1
(
1
r
2
+
5
r
+
7
)
\sum_{r=1}^{\infty} \tan^{-1}\left(\frac{1}{r^2 + 5r + 7}\right)
∑
r
=
1
∞
tan
−
1
(
r
2
+
5
r
+
7
1
)
is equal to a.
tan
−
1
3
\tan^{-1}3
tan
−
1
3
b.
π
4
\frac{\pi}{4}
4
π
c.
sin
−
1
1
10
\sin^{-1}\frac{1}{\sqrt{10}}
sin
−
1
10
1
d.
cot
−
1
2
\cot^{-1}2
cot
−
1
2
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