Answer
The sequence $b_n$ converges to $\pi/4$.
Work Step by Step
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 $\pi/4$.
