The value of \( \cot \left(\sum_{n=1}^{23} \cot ^{-1}\left(1+\sum_{k=1}^{n} 2 k\right)\right) \)...

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The value of \( \cot \left(\sum_{n=1}^{23} \cot ^{-1}\left(1+\sum_{k=1}^{n} 2 k\right)\right) \) is
 
(A) \( \frac{23}{25} \)
(B) \( \frac{25}{23} \)
(C) \( \frac{23}{24} \)
(D) \( \frac{24}{23} \)
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