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 \(100m+10n+p\).
(第二十届AIME2 2002 第11题)