Recallthat |an-L| <εmeansthe valuesofansuchthatL-ε<an<L+ε.
Whatdoesthe definitionof the limit of a sequencemean?Hereis anotherexample.
Example 5
Lookat Figure3.
Figure3 showsthe graphof the sequence. Noticethat fromNon, the termsof are between
L-εandL+ε. In otherwords,for this valueofε, thereis a valueNsuchthat all termsofanare in the in-
tervalfromL-εandL+ε. Thus,.
Not everysequencehas a limit.
Example 6
Hereis a graphof the sequence{n+ 1}.