\limsup B_i := \bigcap_{n=1}^{\infty}(\bigcup_{k=n}^{\infty} B_k ) = \bigcap_{n=1}^{\infty}(\bigcup_{k=n}^{\infty} [\frac{1}{k},5+\frac{1}{k}] ) = \bigcap_{n=1}^{\infty}(0,5+\frac{1}{n}] = (0,5]