Suppose we perform an infinite sequence of experiments. For k = 1, 2, 3,..., the outcome of the k-th experiment is successful with probability ka, where a is a constant strictly between 0 and 1, but is unsuccessful with probability 1-k-a. Suppose the experiments are mutually independent. Find the probability that we have n consecutive successful experimental outcome infinitely often. (The answer depends on the values of a and n.)