I am having a lot of trouble with the concept of proving the limit of a sequence using epsilon n. As an example, I am working on trying to prove that the limit of the sequnce is . I understand that the first step is to set . I then solve for n and get . So I think I understand this tells me that for any , picking an will give a value less than . I'm just not sure where to go next with the proof. I've arbitraily tried different values than for the limit and every time I can solve arbitrary number for something with in it. So I must be doing something wrong as it seems using my method I can prove the limit to be any arbitrary number. In searching online and other forums it seems there is maybe a last step where I take my and somehow work in the "other direction" to prove that indeed any works, but I've been unable to follow. Thanks for any help.