# Give an example of an unbounded sequence {$x_n$} for which {$y_n$} converges.

Let $\{x_n\}$ be a sequence of real numbers and let $y_n = \max \{x_1, x_2, \ldots , x_n\}$ for each positive integer $n$.

Give an example of an unbounded sequence {$x_n$} for which {$y_n$} converges.

I understand this conceptually but having a difficult time finding such a sequence. Any help would be appreciated!

• Hint: What if the $x_n$'s are negative? – Michael Burr Feb 26 '17 at 23:31
• hmmm i don't think i understand – JxxYsde3 Feb 26 '17 at 23:32
• What if $x_n=-n$? – Michael Burr Feb 26 '17 at 23:33

If $x_n=-n$, then $y_n=-1$, for all $n\in\mathbb N$, and hence $\{y_n\}$ converges.