  We consider a diffusing particle, with diffusion constant D', moving in one
dimension in an infinite sea of noninteracting mobile traps with diffusion
constant D and density rho. We show that the asymptotic behavior of the
survival probability, P(t), is given by P(t) ~ exp[-4 rho(Dt/pi)^{1/2}],
independent of D'. The result comes from obtaining upper and lower bounds on
P(t), and showing that they coincide asymptotically. We also obtain exact
results for P(t) to first order in D' for an arbitrary finite number of traps.
