The number of particles emitted as the result of an experiment is a random variable with probability distribution:
What is the expected number of particles emitted during one experiment
This is how I've gone so far:
I'm confused as to how to evaluate this sum
im pretty rusty on infinite sums and it would be interesting to know if there is a closed form summation of that.
Nevertheless, you dont need to do anything difficult to solve this problem. You can rewrite as follows:
This is the PF of a geometric distribution with p=0.5. The mean of a geometric distribution is a standard result:
edit too slow
Yes. (Verification is simple using the well known formula given here: Geometric distribution - Wikipedia, the free encyclopedia).