Question

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

• A. $\frac{23}{25}$
• B. $\frac{25}{23}$
• C. $\frac{23}{24}$
• D. $\frac{24}{23}$

Hint:

Logic Tip: Telescoping series in inverse trigonometry almost always rely on algebraic manipulation of the numerator to match the factors of the denominator's second term. If the denominator is $1+A$, factor $A$ into $x \cdot y$ such that $x-y = \text{numerator}$.

Answer 1

The Correct Option is B