If \( \cot ^{-1}(\alpha)=\cot ^{-1} 2+\cot ^{-1} 8+\cot ^{-1} 18+\c...

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If \( \cot ^{-1}(\alpha)=\cot ^{-1} 2+\cot ^{-1} 8+\cot ^{-1} 18+\cot ^{-1} 32+\ldots . \). upto 100 terms, then \( \alpha \) is :
[JEE Main-2021 (March)]
\( \mathrm{P} \)
(a) \( 1.02 \)
(b) \( 1.03 \)
(c) \( 1.01 \)
(d) \( 1.00 \)
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