Solution
We can graphthe correspondingfunction forn= 1, 2, 3,.... The graphof is similarto the con-
tinuousfunction for the domainofx≥ 1.
To determinethe limit, we look at the trendor behaviorof the graphof sequenceas n gets largeror travels
out to positiveinfinity. This meanswe look at the pointsof sequencethat correspondto the far right end of
the horizontalaxis in the figureon the right.We see that the pointsof the sequenceare gettingcloserto the
horizontalaxis,y= 0. Thus,the limit of the sequence is 0 asntendsto infinity. We write:
.
Hereis the precisedefinitionof the limit of a sequence.
Limitof a SequenceThelimit of a sequenceanis the numberLif for eachε> 0, thereexists
an integerNsuchthat |an-L| <εfor alln>N.