1. The problem statement, all variables and given/known data I need to understand as to why the following series fn(x) = x/(1+n*x^2) is point wise convergent (as mentioned in the book of Ross) and not [obviously] uniformly convergent. 2. Relevant equations The relevant equation used is that lim (n-> infinity) sup|(fn(x) - f(x))|= 0 implies uniform convergent.---- (1) 3. The attempt at a solution It is obvious lim (n-> infinity) fn(x) = f(x) = 0 for x not equal to zero. And when x=0, fn(0) = 0 and hence as n-> infinity, fn(0) = f(0) =0. As mentioned in Ross and ( I can see) that fn(x) is pointwise convergent. But, it looks like for all x, the function fn(x) converges to f(x)=0. So, I am unclear as to why it is not uniform convergent? Please clarify. The book further uses the theorem (1) to prove uniform converfence, which I can understand.