B = \left\{ \cos (2k\pi)\cdot \displaystyle\frac{2k+1}{2k}:k\in\mathbb{N} \right\} \cup \left\{ \cos (2k-1)\pi \cdot \displaystyle\frac{2k}{2k-1}:k\in\mathbb{N} \right\} \\ = \left\{ 1 + \displaystyle\frac{1}{2k} :k\in\mathbb{N}\right\} \cup \left\{ -1 - \displaystlye\frac{1}{2k-1}:k\in\mathbb{N} \right\} \implies \sup B = \displaystlye\frac{3}{2}, \quad\inf B = -2