JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
If \(S\) is the sum of the first \(10\) terms of the series \(\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{13}\right)+\tan ^{-1}\left(\frac{1}{21}\right)+\ldots\) then \(\tan ( S )\) is equal to
- A \(\frac{5}{11}\)
- B \(-\frac{6}{5}\)
- C \(\frac{10}{11}\)
- D \(\frac{5}{6}\)
Answer & Solution
Correct Answer
(D) \(\frac{5}{6}\)
Step-by-step Solution
Detailed explanation
\(S=\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{13}\right)+\ldots\) \(S=\tan ^{-1}\left(\frac{2-1}{1+1.2}\right)+\tan ^{-1}\left(\frac{3-2}{1+2 \times 3}\right)+\tan ^{-1}\)…
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