The value of cot(∑n=123cot−1(1+∑k=1n2k)) is k then 23k=

cot(∑n=123cot−1(n2+n+1))⇒cot(∑n=123tan−1(n+1−n1+n(n+1)))⇒cot(tan−1(24)-tan-1(1))⇒cot(tan−1(2325))=2523

The value of cot(∑n=123cot−1(1+∑k=1n2k)) is k then 23k=

cot(∑n=123cot−1(n2+n+1))⇒cot(∑n=123tan−1(n+1−n1+n(n+1)))⇒cot(tan−1(24)-tan-1(1))⇒cot(tan−1(2325))=2523

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The value of $\cot (\sum_{n = 1}^{23} \cot^{- 1} (1 + \sum_{k = 1}^{n} 2 k))$ is k then $23 k =$

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$\cot (\sum_{n = 1}^{23} \cot^{- 1} (n^{2} + n + 1)) \Rightarrow \cot (\sum_{n = 1}^{23} \tan^{- 1} (\frac{n + 1 - n}{1 + n (n + 1)}))$

$\Rightarrow \cot (\tan^{- 1} (24) - \tan^{- 1} (1))$
$\Rightarrow \cot (\tan^{- 1} (\frac{23}{25})) = \frac{25}{23}$

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The value of cot(∑n=123cot−1(1+∑k=1n2k)) is k then 23k=

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The value of $\cot (\sum_{n = 1}^{23} \cot^{- 1} (1 + \sum_{k = 1}^{n} 2 k))$ is k then $23 k =$