Let where . Find
doing it without graphing is not much harder. what happens to 1/n for various values of n? what about 1 + 1/(2n)? how do these change when n gets large?
Isn't the left endpoint getting smaller as k gets bigger?
1, 1/2, 1/3, 1/4, ... , 1/k
All intervals after fit inside of ... So, the arbitrary union of all the intervals would then be the one interval that contains them all... Or, that's how my professor made it seem anyway...
getting smaller means the intervals are "expanding" to the left. the left endpoint keeps getting farther from 1