Suppose that independent trials are performed, with trial being a success with probability 1/(2i + 1). Let P_n denote the probability that the total number of successes that result is an odd number.

a. Find P_n for n = 1, 2, 3, 4, 5.

b. Conjecture a general formula for P_n.

c. Derive a formula for P_n in terms of P_n-1.

d. Verify that your conjecture in part (b) satisfies the recursive formula in part (c). Because the recursive formula has a unique solution, this then proves that your conjecture is correct.