Lower and upper bounds for (sums of) binomial coefficients

Apparently there is no closed form for the partial sum of a row of
Pascal's triangle. In this paper lower and upper bounds for
binomial coefficients and their sums are deduced. In the case of
single coefficients these bounds differ only by a constant factor
which is arbitrarily close to 1 for sufficiently large n. In the
case of sums the gap between lower and upper bound is larger but
still small enough to be useful in some applications. The upper
bound obtained for sums is somewhat better than that resulting
from a Chernoff bound.