1. Tardigrade
  2. Question
  3. Mathematics
  4. displaystyle∑n=3∞ tan -1((4/n2-2 n-2)) is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. $\displaystyle\sum_{n=3}^{\infty} \tan ^{-1}\left(\frac{4}{n^2-2 n-2}\right)$ is equal to

Inverse Trigonometric Functions

Solution:

$\displaystyle\sum_{n=3}^{\infty} \tan ^{-1}\left(\frac{4}{n^2-2 n-2}\right)=\displaystyle\sum_{n=3}^{\infty} \tan ^{-1}\left(\frac{4}{1+(n+1)(n-3)}\right)=\displaystyle\sum_{n=3}^{\infty}\left(\tan ^{-1}(n+1)-\tan ^{-1}(n-3)\right)$
image
$S_{\infty} =2 \pi - \pi = \pi$