AP EAMCET · Maths · Inverse Trigonometric Functions
\(\lim _{n \rightarrow \infty} \sum_{r=1}^n \cot ^{-1}\left(r^2+\frac{3}{4}\right)=\)
- A \(\cot ^{-1} 2\)
- B \(\cot ^{-1} \frac{1}{3}\)
- C \(\tan ^{-1} 2\)
- D \(\tan ^{-1} \frac{1}{3}\)
Answer & Solution
Correct Answer
(C) \(\tan ^{-1} 2\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \lim _{n \rightarrow \infty} \sum_{r=1}^n \cot ^{-1}\left(r^2+\frac{3}{4}\right) \\ & =\lim _{n \rightarrow \infty} \sum_{r=1}^n \tan ^{-1}\left[\frac{1}{r^2+1-\frac{1}{4}}\right] \\ & =\lim _{n \rightarrow \infty} \sum_{r=1}^n \tan…
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