Show that a sequence is bounded

[A dummy progression]

Question : Show that if a sequence un is bounded there exists a real k such that |u|<k.



Here is an image of what i did but i don't know how to go further

 

[blamocur]

You don't need limits for this problem.
Hint: [imath]|u|<k[/imath] is the same as saying that [imath]u <k[/imath] and [imath]-u < k[/imath].

 

[Steven G]

Using the values a and b you need to find k such that |u|<k