Lebl-Basic-Analysis-I · Problem 2.1.15

Sequences and Series

Mathematics · sequences-and-limits

Problem

Let

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

be a sequence defined by

x_n := \begin{cases} n & \text{if } n \text{ is odd,} \\ 1/n & \text{if } n \text{ is even.} \end{cases}

a) Is the sequence bounded? (prove or disprove) b) Is there a convergent subsequence? If so, find it.