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The value of cot(∑ₙ₌₁²³ cot⁻¹(1 + ∑ₖ₌₁ⁿ 2k)) is -

1. 23/25
2. 25/23
3. 23/24
4. 24/23

Correct answer: 25/23

Solution

The given summation simplifies to a telescoping series, and the cotangent of the resulting angle evaluates to 25/23 after applying trigonometric identities.

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