Let .Suppose has the property that: is convergent. Prove that is continuous at .
my approach:
Let and be two sequences in with . let and . I need to prove that . how do i go about it?
You can do this by considering the sequence .
Notice that it is not sufficient just to show that . You need to show that this limit is equal to . You can do that by taking one of your sequences to be the constant sequence for all n.