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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.

Problem Statement