This is my question

Suppose we do n independent trails that each has a probability p E (0, 1) to result in success. Let Pn be the probability that we get even number of success (0 is even). (a) Show that P\" = p(1 Pn_1) + (1 p)P _1 (b) Show that limn_>00 P\" does not depend on p, and nd this limit. (Hint: Show that Pn = 1+(1;2p)")