1990 AIME Problem 9

A fair coin is to be tossed 10_{}^{} times. Let i/j^{}_{}, in lowest terms, be the probability that heads never occur on consecutive tosses. Find i+j_{}^{}.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.