. A coin is tossed repeatedly, and heads turn up with probability p on each toss. Let hn be the probability of an even number of heads in the first n tosses, with the convention that 0 is an even...

. A coin is tossed repeatedly, and heads turn up with probability p on each toss. Let hn be the probability of an even number of heads in the first n tosses, with the convention that 0 is an even number. Find a difference equation for the hn and deduce that they have a generating function