  We use Stein's method to prove a generalization of the Lindeberg-Feller CLT
providing an upper and a lower bound for the superior limit of the Kolmogorov
distance between a normally distributed random variable and the rowwise sums of
a rowwise independent triangular array of random variables which is
asymptotically negligible in the sense of Feller. A natural example shows that
the upper bound is of optimal order. The lower bound improves a result by
Andrew Barbour and Peter Hall.
