Calculus (3rd Edition)

The sequence $b_n$ converges to $\pi/4$.
We have $$\lim_{n\to \infty}b_n=\lim_{n\to \infty} \tan ^{-1}\left(1-\frac{2}{n}\right) \\ =\tan ^{-1}\left(1-0\right)=\pi/4.$$ Hence, by Theorem 1, the sequence $b_n$ converges to $\pi/4$.