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Sum of tan^-1(1/(2r^2)), the same as cot^-1 2 + cot^-1 8 + cot^-1 18 + ...

The same question, asked 2 times: 2021 Paper 7*, 2021 Paper 19. Every wording below, oldest first.

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  1. Question 1

    2021 Paper 7

    65
    If cot⁡−1(α)=cot⁡−12+cot⁡−18+cot⁡−118\cot^{- 1}(\alpha) =\cot^{- 1}2 +\cot^{- 1}8 +\cot^{- 1}18 +cot⁡−132+…+\cot^{- 1}32 + \ldots. upto 100 terms, then α\alpha is :

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  2. Question 2

    2021 Paper 19

    70
    If ∑r=150tan⁡−112r2=p\sum_{r = 1}^{50} \tan^{- 1}\frac{1}{2r^{2}}= p, then the value of tan⁡p\tan p is :

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