The limits on an as n goes to infinity is aThen for some epsilon greater than 0, chose N such that for n>Nwe have |an-a| < epsilon.Now if m and n are > N we have |an-am|=|(am -a)-(an...
A convergent sequence is an infinite sequence whose terms move ever closer to a finite limit. For any specified allowable margin of error (the absolute difference between each term and the finite...
It could be divergent eg 1+1+1+1+...Or, it could be oscillating eg 1-1+1-1+ ...So there is no definition for a sequence that is not convergent except non-convergent.
