A group of 10 hunters wait for ducks to fly by. When a flock of ducks flies overhead, the hunters all fire at the same time, each selecting a target at random and independently of the others. If each hunter independently hits his target with probability 0.5, and if all misses do not hit other ducks, what is the expected number of ducks that will be hit? Assume that the number of ducks in a flock is a Poisson random variable with mean 5.

$E[N] =$
(Hint: your final answer will involve a sum; you may want to approximate it with a partial sum. If you do this, be sure to include at least 8 terms.)