Comprehension : We know Inverse trigonometric function have defined domain \( \& \) range \( \&[...

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Comprehension
: We know Inverse trigonometric function have defined domain \( \& \) range \( \&[x] \) denotes greatest integer less than or equals to \( x \). Answer the following
The sum of series
\( \sec ^{-1} \sqrt{2}+\sec ^{-1} \frac{\sqrt{10}}{3}+\sec ^{-1} \frac{\sqrt{50}}{7}+\ldots . \).
\( \ldots+\sec ^{-1} \sqrt{\frac{\left(n^{2}+1\right)\left(n^{2}-2 n+2\right)}{\left(n^{2}-n+1\right)^{2}}} \) is
(a) \( \tan ^{-1} 1 \)
(b) \( \tan ^{-1} n \)
(c) \( \tan ^{-1}(n+1) \)
(d) \( \tan ^{-1}(n-1) \)
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