2002 AIME II Problem 11

Two distinct, real, infinite geometric series each have a sum of 1 and have the same second term. The third term of one of the series is 1 / 8, and the second term of both series can be written in the form \frac{\sqrt{m}-n}{p}, where m, n, and p are positive integers and m is not divisible by the square of any prime. Find 100 m+10 n+p.