Basic Analysis I — Real Analysis · Problem 2.3.1

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · limit-superior-limit-inferior

Problem

Suppose

\{x_n\}_{n=1}^\infty

is a bounded sequence. Define

a_n

and

b_n

as in Definition 2.3.1. Show that

\{a_n\}_{n=1}^\infty

and

\{b_n\}_{n=1}^\infty

are bounded.