  We investigate the approximation for computing the sum $a_1+...+a_n$ with an
input of a list of nonnegative elements $a_1,..., a_n$. If all elements are in
the range $[0,1]$, there is a randomized algorithm that can compute an
$(1+\epsilon)$-approximation for the sum problem in time ${O({n(\log\log
n)\over\sum_{i=1}^n a_i})}$, where $\epsilon$ is a constant in $(0,1)$. Our
randomized algorithm is based on the uniform random sampling, which selects one
element with equal probability from the input list each time. We also prove a
lower bound $\Omega({n\over \sum_{i=1}^n a_i})$, which almost matches the upper
bound, for this problem.
