Pointwise Convergence of Sequence fn(x) = (x-1/n)^2 on [0,1]

Yes, the sequence converges pointwise on the set [0,1] to the function f(x) = x^2.

To see this, consider the limit of fn(x) as n approaches infinity for any fixed x in [0,1]:

lim(n->inf) fn(x) = lim(n->inf) (x-1/n)^2 = (lim(n->inf) (x-1/n))^2 = (x-0)^2 = x^2

Thus, for any x in [0,1], the sequence fn(x) converges to x^2 as n approaches infinity.