Let { a n } n = 1 ∞ {\displaystyle \{a_{n}\}_{n=1}^{\infty }} be a bounded sequence of real numbers. For each n ∈ N {\displaystyle n\in \mathbb {N} } define
Prove that { b n } n = 1 ∞ {\displaystyle \{b_{n}\}_{n=1}^{\infty }} is a convergent sequence. (You may use part (a)).
